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Radioactive decay

For particle decay in a more general context see Particledecay For more information on hazards of various kindsof radiation from decay see Ionizing radiationldquoRadioactiverdquo redirects here For other uses seeRadioactive (disambiguation)ldquoRadioactivityrdquo redirects here For other uses seeRadioactivity (disambiguation)

Radioactive decay also known as nuclear decay or

Alpha decay is one type of radioactive decay in which an atomic

nucleus emits an alpha particle and thereby transforms (or ldquode-caysrdquo) into an atom with a mass number decreased by 4 and

atomic number decreased by 2

radioactivity is the process by which a nucleus of anunstable atom loses energy by emitting radiation A ma-terial that spontaneously emits such radiation mdash whichincludes alpha particles beta particles gamma rays andconversion electrons mdash is considered radioactive

Radioactive decay is a stochastic (ie random) process atthe level of single atoms in that according to quantumtheory it is impossible to predict when a particular atom

will decay[1][2][3][4] The chance that a given atom will de-cay never changes that is it does not matter how long theatom has existed For a large collection of atoms how-ever the decay rate for that collection can be calculatedfrom their measured decay constants or half-lives This isthe basis of radiometric dating The half-lives of radioac-tive atoms have no known limits for shortness or length ofduration and range over 55 orders of magnitude in time

There are many types of radioactive decay (see table be-low) A decay or loss of energy from the nucleus re-sults when an atom with one type of nucleus called the

parent radionuclide (or parent radioisotope[note 1]) trans-

forms into an atom with a nucleus in a different state orwith a nucleus containing a different number of protonsand neutrons The product is called the daughter nuclide

In some decays the parent and the daughter nuclides aredifferent chemical elements and thus the decay processresults in the creation of an atom of a different elementThis is known as a nuclear transmutation

The first decay processes to be discovered were alphadecay beta decay and gamma decay Alpha decay oc-curs when the nucleus ejects an alpha particle (heliumnucleus) This is the most common process of emittingnucleons but in rarer types of decays nuclei can ejectprotons or in the case of cluster decay specific nuclei

of other elements Beta decay occurs when the nucleusemits an electron or positron and a neutrino in a pro-cess that changes a proton to a neutron or the other wayabout The nucleus may capture an orbiting electroncausing a proton to convert into a neutron in a processcalled electron capture All of these processes result in awell-defined nuclear transmutation

By contrast there are radioactive decay processes that donot result in a nuclear transmutation The energy of an ex-cited nucleus may be emitted as a gamma ray in a processcalled gamma decay or be used to eject an orbital elec-tron by its interaction with the excited nucleus in a pro-

cess called internal conversion Highly excited neutron-rich nuclei formed as the product of other types of de-cay occasionally lose energy by way of neutron emissionresulting in a change of an element from one isotope toanother

Another type of radioactive decay results in productsthat are not defined but appear in a range of ldquopiecesrdquoof the original nucleus This decay called spontaneousfission happens when a large unstable nucleus sponta-neously splits into two (and occasionally three) smallerdaughter nuclei and generally leads to the emission ofgamma rays neutrons or other particles from those prod-

uctsFor a summary table showing the number of stable andradioactive nuclides in each category see radionuclideThere exist twenty-nine chemical elements on Earth thatare radioactive They are those that contain thirty-fourradionuclides that date before the time of formation ofthe solar system and are known as primordial nuclidesWell-known examples are uranium and thorium but alsoincluded are naturally occurring long-lived radioisotopessuch as potassium-40 Another fifty or so shorter-livedradionuclides such as radium and radon found on Earthare the products of decay chains that began with the

primordial nuclides and ongoing cosmogenic processessuch as the production of carbon-14 from nitrogen-14 by

1



2 2 EARLY HEALTH DANGERS

cosmic rays Radionuclides may also be produced artifi-cially in particle accelerators or nuclear reactors resultingin 650 of these with half-lives of over an hour and sev-eral thousand more with even shorter half-lives See thislist of nuclides for a list of these sorted by half life

1 History of discovery

Pierre and Marie Curie in their Paris laboratory before 1907

Radioactivity was discovered in 1896 by the Frenchscientist Henri Becquerel while working withphosphorescent materials[5] These materials glow

in the dark after exposure to light and he suspectedthat the glow produced in cathode ray tubes by X-raysmight be associated with phosphorescence He wrappeda photographic plate in black paper and placed variousphosphorescent salts on it All results were negativeuntil he used uranium salts The uranium salts causeda blackening of the plate in spite of the plate beingwrapped in black paper These radiations were given thename ldquoBecquerel Raysrdquo

It soon became clear that the blackening of the plate hadnothing to do with phosphorescence as the blackeningwas also produced by non-phosphorescent salts of ura-

nium and metallic uranium It became clear from theseexperiments that there was a form of invisible radiationthat could pass through paper and was causing the plateto react as if exposed to light

At first it seemed as though the new radiation was sim-ilar to the then recently discovered X-rays Further re-search by Becquerel Ernest Rutherford Paul VillardPierre Curie Marie Curie and others showed that thisform of radioactivity was significantly more complicatedRutherford was the first to realize that all such elementsdecay in accordance with the same mathematical expo-nential formula Rutherford and his student Frederick

Soddy were the first to realize that many decay processesresulted in the transmutation of one element to anotherSubsequently the radioactive displacement law of Fajans

and Soddy was formulated to describe the products ofalpha and beta decay[6][7]

The early researchers also discovered that many otherchemical elements besides uranium have radioactiveisotopes A systematic search for the total radioactivity

in uranium ores also guided Pierre and Marie Curie toisolate two new elements polonium and radium Exceptfor the radioactivity of radium the chemical similarityof radium to barium made these two elements difficult todistinguish

2 Early health dangers

Main article ionizing radiationThedangers of ionizing radiationdue to radioactivity and

Taking an X-ray image with early Crookes tube apparatus in

1896 The Crookes tube is visible in the centre The standingman is viewing his hand with a fluoroscope screen this was a

common way of setting up the tube No precautions against ra-

diation exposure are being taken its hazards were not known at

the time

X-rays were not immediately recognized

21 X-rays

The discovery of x‑rays by Wilhelm Roumlntgen in 1895 ledto widespread experimentation by scientists physicians

and inventors Many people began recounting stories ofburns hair loss and worse in technical journals as earlyas 1896 In February of that year Professor Daniel andDr Dudley of Vanderbilt University performed an ex-periment involving X-raying Dudleyrsquos head that resultedin his hair loss A report by Dr HD Hawks of his suf-fering severe hand and chest burns in an X-ray demon-stration was the first of many other reports in Electrical

Review[8]

Other experimenters including Elihu Thomson andNikola Tesla also reported burns Thomson deliberatelyexposed a finger to an X-ray tube over a period of time

and suffered pain swelling and blistering[9] Other ef-fects including ultraviolet rays and ozone were some-times blamed for the damage[10] and many physicians



3

still claimed that there were no effects from X-ray ex-posure at all[9]

Despite this there were some early systematic hazard in-vestigations andas early as 1902 William Herbert Rollinswrote almost despairingly that his warnings about the

dangers involved in careless use of X-rays was not be-ing heeded either by industry or by his colleagues Bythis time Rollins had proved that X-rays could kill ex-perimental animals could cause a pregnant guinea pig toabort and that they could kill a fetus[11] He also stressedthat ldquoanimals vary in susceptibility to the external actionof X-lightrdquo and warned that these differences be consid-ered when patients were treated by means of X-rays

22 Radioactive substances

Radioactivity is characteristic of elements with large atomic num-

ber Elements with at least one stable isotope are shown in light

blue Green shows elements whose most stable isotope has a

half-life measured in millions of years Yellow and orange are

progressively more unstable with half-lives in thousands or hun-

dreds of years down toward one day Red and purple show

highly and extremely radioactive elements where the most stable

isotopes exhibit half-lives measured on the order of one day and

much less

However the biological effects of radiation due to ra-dioactive substances were less easy to gauge This gavethe opportunity for many physicians and corporationsto market radioactive substances as patent medicinesExamples were radium enema treatments and radium-containing waters to be drunk as tonics Marie Curieprotested against this sort of treatment warning that theeffects of radiation on the human body were not well un-derstood Curie later died from aplastic anaemia likely

caused by exposure to ionizing radiation By the 1930safter a number of cases of bone necrosis and death ofradium treatment enthusiasts radium-containing medic-inal products had been largely removed from the market(radioactive quackery)

23 Radiation protection

Main article Radiation protectionSee also Sievert and Ionizing radiation

Only a year after Roumlntgenrsquos discovery of X rays theAmerican engineer Wolfram Fuchs (1896) gave what isprobably the first protection advice but it was not until

1925 that the first International Congress of Radiology(ICR) was held and considered establishing internationalprotection standards The effects of radiation on genesincluding the effect of cancer risk were recognized muchlater In 1927 Hermann Joseph Muller published re-search showing genetic effects and in 1946 was awarded

the Nobel prize for his findingsThe second ICR was held in Stockholm in 1928 andproposed the adoption of the rontgen unit and the In-ternational X-ray and Radium Protection Committee(IXRPC) was formed Rolf Sievert was named Chair-man but a driving force was George Kaye of the BritishNational Physical Laboratory The committee met in1931 1934 and 1937

After World War II the increased range and quantity ofradioactive substances being handled as a result of mil-itary and civil nuclear programmes led to large groups

of occupational workers and the public being potentiallyexposed to harmful levels of ionising radiation This wasconsidered at the first post-war ICR convened in Londonin 1950 when the present International Commission onRadiological Protection (ICRP) was born[12] Since thenthe ICRP has developed the present international systemof radiation protection covering all aspects of radiationhazard

3 Units of radioactivity

Graphic showing relationships between radioactivity and de-

tected ionizing radiation

The International System of Units (SI) unit of radioac-tive activity is the becquerel (Bq) named in honour ofthe scientist Henri Becquerel One Bq is defined as onetransformation (or decay or disintegration) per second

An older unit of radioactivity is the curie Ci which wasoriginally defined as ldquothe quantity or mass of radiumemanation in equilibrium with one gram of radium

(element)[13] Today the curie is defined as 37times1010disintegrations persecond so that 1 curie (Ci) = 37times1010

Bq For radiological protection purposes although the



4 4 TYPES OF DECAY

United States Nuclear Regulatory Commission permitsthe use of the unit curie alongside SI units[14] theEuropean Union European units of measurement direc-tives required that its use for ldquopublic health purposesrdquobe phased out by 31 December 1985[15]

4 Types of decay

α

β

γ

Alpha particles may be completely stopped by a sheet of paper

beta particles by aluminium shielding Gamma rays can only

be reduced by much more substantial mass such as a very thick

layer of lead

Early researchers found that an electric or magneticfield could split radioactive emissions into three typesof beams The rays were given the names alpha betaand gamma in order of their ability to penetrate mat-

ter While alpha decay was seen only in heavier elementsof atomic number 52 (tellurium) and greater the othertwo types of decay were produced by all of the elementsLead atomic number 82 is the heaviest element to haveany isotopes stable (to the limit of measurement) to ra-dioactive decay Radioactive decay is seen in all isotopesof all elements of atomic number 83 (bismuth) or greaterBismuth however is only very slightly radioactive

In analysing the nature of the decay products it was obvi-ous from the direction of the electromagnetic forces ap-plied to the radiations by external magnetic and electricfields that alpha particles carried a positive charge beta

particles carried a negative charge and gamma rays wereneutral From the magnitude of deflection it was clearthat alpha particles were much more massive than beta

N

Z

Parent

atom

α

β minus

n

p

β +EC

Transition diagram for decay modes of a radionuclide with neu-

tron number N and atomic number Z (shown are α βplusmn p+ and

n0 emissions EC denotes electron capture)

Types of radioactive decay related to N and Z numbers

particles Passing alpha particles through a very thin glasswindow and trapping them in a discharge tube allowed re-searchers to study the emission spectrum of the capturedparticles and ultimately proved that alpha particles are

helium nuclei Other experiments showed beta radiationresulting from decay and cathode rays were high-speedelectrons Likewise gamma radiation and X-rays were



5

found to be high-energy electromagnetic radiation

The relationship between the types of decays also beganto be examined For example gamma decay was almostalways found to be associated with other types of de-cay and occurred at about the same time or afterwards

Gamma decay as a separate phenomenon with its ownhalf-life (now termed isomeric transition) was found innatural radioactivity to be a result of the gamma decay ofexcited metastable nuclear isomers which were in turncreated from other types of decay

Although alpha beta and gamma radiations were mostcommonly found other types of emission were even-tually discovered Shortly after the discovery of thepositron in cosmic ray products it was realized that thesame process that operates in classical beta decay canalso produce positrons (positron emission) along withneutrinos (classical beta decay produces antineutrinos)

In a more common analogous process called electroncapture some proton-rich nuclides were found to capturetheir own atomic electrons instead of emitting positronsand subsequently these nuclides emit only a neutrino anda gamma ray from the excited nucleus (and often alsoAuger electrons and characteristic X-rays as a result ofthe re-ordering of electrons to fill the place of the miss-ing captured electron) These types of decay involve thenuclear capture of electrons or emission of electrons orpositrons and thus acts to move a nucleus toward the ra-tio of neutrons to protons that has the least energy for agiven total number of nucleons This consequently pro-duces a more stable (lower energy) nucleus

(A theoretical process of positron capture analogous toelectron capture is possible in antimatter atoms but hasnot been observed as complex antimatter atoms (beyondantihelium) are not experimentally available[16] Such adecay would require antimatter atoms at least as com-plex as beryllium-7 which is the lightest known isotopeof normal matter to undergo decay by electron capture)

Shortly after the discovery of the neutron in 1932 EnricoFermi realized that certain rare beta-decay reactions im-mediately yield neutrons as a decay particle (neutronemission) Isolated proton emission was eventually ob-served in some elements It was also found that someheavy elements may undergo spontaneous fission intoproducts that vary in composition In a phenomenoncalled cluster decay specific combinations of neutronsand protons other than alpha particles (helium nuclei)were found to be spontaneously emitted from atoms

Other types of radioactive decay were found to emitpreviously-seen particles but via different mechanismsAn example is internal conversion which results inan initial electron emission and then often furthercharacteristic X-rays and Auger electrons emissions al-though the internal conversion process involves neitherbeta nor gamma decay A neutrino is not emitted andnone of the electron(s) and photon(s) emitted originatein the nucleus even though the energy to emit all of

them does originate there Internal conversion decay likeisomeric transition gamma decay and neutron emissioninvolves the release of energy by an excited nuclide with-out the transmutation of one element into another

Rare events that involve a combination of two beta-decay

type events happening simultaneously are known (see be-low) Any decay process that does not violate the conser-vation of energy or momentum laws (and perhaps otherparticle conservation laws) is permitted to happen al-though not all have been detected An interesting exam-ple discussed in a final section is bound state beta decayof rhenium-187 In this process beta electron-decay ofthe parent nuclide is not accompanied by beta electronemission because thebeta particle has been captured intothe K-shell of the emitting atom An antineutrino is emit-ted as in all negative beta decays

Radionuclides can undergo a number of different reac-

tions These are summarized in the following table Anucleus with mass number A and atomic number Z isrepresented as (A Z ) The column ldquoDaughter nucleusrdquoindicates the difference between the new nucleus and theoriginal nucleus Thus (A minus 1 Z ) means that the massnumber is one less than before but the atomic number isthe same as before

If energy circumstances are favorable a given radionu-clide may undergo many competing types of decay withsome atoms decaying by one route and others decayingby another An example is copper-64 which has 29 pro-tons and 35 neutrons which decays with a half-life ofabout 127 hours This isotope has one unpaired protonand one unpaired neutron so either the proton or the neu-tron can decay to the opposite particle This particularnuclide (though not all nuclides in this situation) is al-most equally likely to decay through proton decay pro-ducing a positron emission (18) or through electroncapture (43) as it does through neutron decay by elec-tron emission (39) The excited energy states resultingfrom these decays which fail to end in a ground energystate also produce later internal conversion and gammadecay in almost 05 of the time

Radioactive decay results in a reduction of summed restmass once the released energy (the disintegration en-

ergy) has escaped in some way Although decay energy issometimes defined as associated with the difference be-tween the mass of the parent nuclide products and themass of the decay products this is true only of rest massmeasurements where some energy has been removedfrom the product system This is true because the de-cay energy must always carry mass with it wherever itappears (see mass in special relativity) according to theformula E = mc 2 The decay energy is initially releasedas the energy of emitted photons plus the kinetic energyof massive emitted particles (that is particles that haverest mass) If these particles come to thermal equilib-

rium with their surroundings and photons are absorbedthen the decay energy is transformed to thermal energy



6 6 MATHEMATICS OF RADIOACTIVE DECAY

which retains its mass

Decay energy therefore remains associated with a certainmeasure of mass of the decay system called invariantmass which does not change during the decay eventhough the energy of decay is distributed among decay

particles The energy of photons the kinetic energy ofemitted particles and later the thermal energy of thesurrounding matter all contribute to theinvariant mass ofthe system Thus while the sum of the rest masses of theparticles is not conserved in radioactive decay the system

mass and system invariant mass (and also the system totalenergy) is conserved throughout any decay process Thisis a restatement of the equivalent laws of conservation ofenergy and conservation of mass

5 Radioactive decay rates

The decay rate or activity of a radioactive substance ischaracterized by

Constant quantities

bull The half-lifemdasht ₁₂ is the time taken for the activ-ity of a given amount of a radioactive substance todecay to half of its initial value see List of nuclides

bull The decay constant mdash λ lambda the inverse of themean lifetime sometimes referred to as simply de-

cay rate

bull The mean lifetimemdash τ tau the average lifetime ofa radioactive particle before decay

Although these are constants they are associated with thestatistical behavior of populations of atoms In conse-quence predictions using these constants are less accu-rate for minuscule samples of atoms

In principle a half-life a third-life or even a (1radic2)-lifecan be used in exactly the same way as half-life but themean life and half-life t ₁₂ have been adopted as standardtimes associated with exponential decay

Time-variable quantities

bull Total activitymdash A is the number of decays per unittime of a radioactive sample

bull Number of particles mdashN is the total number of par-ticles in the sample

bull Specific activitymdashSA number of decays per unittime per amount of substance of the sample at timeset to zero (t = 0) ldquoAmount of substancerdquo can be

the mass volume or moles of the initial sample

These are related as follows

t12 = ln(2)

λ = τ ln(2)

A = minusdN dt

= λN

S Aa0 = minusdN dt

t=0

= λN 0

where N 0 is the initial amount of active substance mdash sub-stance that has the same percentage of unstable particlesas when the substance was formed

6 Mathematics of radioactive de-

cay

For the mathematical details of exponential decay ingeneral context see exponential decayFor related derivations with some further details seehalf-lifeFor the analogous mathematics in 1st order chemicalreactions see Consecutive reactions

61 Universal law of radioactive decay

Radioactivity is one very frequently given example ofexponential decay The law describes the statistical be-

haviour of a large number of nuclides rather than indi-vidual atoms In the following formalism the number ofnuclides or the nuclide population N is of course a dis-crete variable (a natural number)mdashbut for any physicalsample N is so large that it can be treated as a continuousvariable Differential calculus is needed to set up differ-ential equations for the modelling the behaviour of thenuclear decay

The mathematics of radioactive decay depend on a keyassumption that a nucleus of a radionuclide has no ldquomem-oryrdquo or way of translating its history into its present be-havior A nucleus does not ldquoagerdquo with the passage of

time Thus the probability of its breaking down doesnot increase with time but stays constant no matter howlong the nucleus has existed This constant probabilitymay vary greatly between different types of nuclei lead-ing to the many different observed decay rates Howeverwhatever the probability is it does not change This is inmarked contrast to complex objects which do show agingsuch as automobiles and humans These systems do havea chance of breakdown per unit of time that increasesfrom the moment they begin their existence

611 One-decay process

Consider the case of a nuclide A that decays into anotherB by some process A rarr B (emission of other particles



61 Universal law of radioactive decay 7

like electron neutrinos νe and electrons eminus as in beta decay are irrelevant in whatfollows) The decay of an unstable nucleus is entirely ran-dom and it is impossible to predict when a particular atomwill decay[1] However it is equally likely to decay at anyinstant in time Therefore given a sample of a particular

radioisotope the number of decay events minusdN expectedto occur in a small interval of time dt is proportional tothe number of atoms present N that is[17]

minusdN dt prop N

Particular radionuclides decay at different rates so eachhas its own decay constant λ The expected decay minusdN N

is proportional to an increment of time dt

The negative sign indicates that N decreases as time in-creases as the decay events follow one after anotherThe solution to this first-order differential equation is thefunction

N (t) = N 0 eminusλt = N 0 e

minustτ

where N 0 is the value of N at time t = 0[17]

We have for all time t

N A + N B = N total = N A0

where N ₒa is theconstant numberof particles throughoutthe decay process which is equal to the initial number ofA nuclides since this is the initial substance

If the number of non-decayed A nuclei is

N A = N A0eminusλt

then the number of nuclei of B ie the number of de-cayed A nuclei is

N B = N A0minusN A = N A0minusN A0eminusλt = N A0

10486161 minus eminusλt

1048617

The number of decays observed over a given intervalobeys Poisson statistics If the average number of decaysis ltNgt the probability of a given number of decays N

is[17]

P (N ) = ⟨N ⟩N exp(minus⟨N ⟩)

N

612 Chain-decay processes

Chain of two decays

Now consider the case of a chain of two decays one nu-clide A decaying into another B by one process then B

decaying into another C by a second process ie A rarr

B rarr C The previous equation cannot be applied to thedecay chain but can be generalized as follows Since A

decays into B then B decays into C the activity of A addsto the total number of B nuclides in the present samplebefore those B nuclides decay and reduce the number ofnuclides leading to the later sample In other words thenumber of second generation nuclei B increasesas a resultof the first generation nuclei decay of A and decreases asa result of its own decay into the third generation nucleiC [18] The sum of these two terms gives the law for a de-cay chain for two nuclides

dN Bdt

= minusλBN B + λAN A

The rate of change of NB that is dNB dt is related to thechanges in the amounts of A and B NB can increase as B

is produced from A and decrease as B produces C

Re-writing using the previous results

The subscripts simply refer to the respective nuclides ie

NA is the number of nuclides of type A N A₀ is the initialnumber of nuclides of type A λA is the decay constantfor A - and similarly for nuclide B Solving this equationfor NB gives

N B = N A0λA

λB minus λA

1048616eminusλAt minus eminusλBt

1048617

In the case where B is a stable nuclide ( λB = 0) this equa-tion reduces to the previous solution

limλBrarr0

983131 N A0λAλB minus λA


1048617983133 = N A0λA

0 minus λA

1048616eminusλAt minus 1

1048617 = N A0

10486161

as shown above for one decay The solution can be foundby the integration factor method where the integratingfactor is eλBt This case is perhaps the most useful sinceit can derive both the one-decay equation (above) and theequation for multi-decay chains (below) more directly

Chain of any number of decays

For the general case of any number of consecutive decaysin a decay chain ie A1 rarr A2 middotmiddotmiddot rarr Ai middotmiddotmiddot rarr AD whereD is the number of decays and i is a dummy index (i = ₁ ₂

₃ D ) each nuclide population can be found in terms ofthe previous population In this case N 2 = 0 N 3 = 0ND = 0 Using the above result in a recursive form




dN jdt

= minusλjN j + λjminus1N (jminus1)0eminusλjminus1t

The general solution to the recursive problem is given byBatemanrsquos equations[19]

613 Alternative decay modes

In all of the above examples the initial nuclide decaysinto only one product[20] Consider the case of one initialnuclide that can decay into either of two products that isA rarr B and A rarr C in parallel For example in a sample ofpotassium-40 893 of the nuclei decay to calcium-40and 107 to argon-40 We have for all time t

N = N A + N B + N C

which is constant since the total number of nuclides re-mains constant Differentiating with respect to time

dN Adt

= minus

983080dN B

dt +

dN C dt

983081

minusλN A = minusN A (λB + λC )

defining the total decay constant λ in terms of the sum of partial decay constants λB and λC

λ = λB + λC

Notice that

dN Adt

lt 0 dN B

dt gt 0

dN C dt

gt 0

Solving this equation for NA

N A = N A0eminusλt

where NA₀ is the initial number of nuclide A When mea-suring the production of one nuclide one can only ob-serve the total decay constant λ The decay constants λB

and λC determine the probability for the decay to resultin products B or C as follows

N B = λB

λ N A0


1048617

N C = λC

λ

N A0 10486161 minus eminusλt1048617 because the fraction λB λ of nuclei decay into B while thefraction λC λ of nuclei decay into C

62 Corollaries of the decay laws

The above equations can also be written using quantitiesrelated to the number of nuclide particles N in a sample

bull The activity A = λN

bull The amount of substance n = NL

bull The mass M = Arn = ArNL

where L = 6022times1023 is Avogadrorsquos constant Ar is therelative atomic mass number and the amount of the sub-stance is in moles

63 Decay timing definitions and relations

631 Time constant and mean-life

For the one-decay solution A rarr B

N = N 0 eminusλt = N 0 e

minustτ

the equation indicates that the decay constant λ has unitsof t minus1 and can thus also be represented as 1τ where τ is acharacteristic time of the process called the time constant

In a radioactive decay process this time constant is alsothe mean lifetime for decaying atoms Each atom ldquolivesrdquofor a finite amount of time before it decays and it may

be shown that this mean lifetime is the arithmetic meanof all the atomsrsquo lifetimes and that it is τ which again isrelated to the decay constant as follows

τ = 1

λ

This form is also true for two-decay processes simultane-ously A rarr B + C inserting the equivalent values of decayconstants (as given above)

λ = λB + λC

into the decay solution leads to

1

τ = λ = λB + λC =

1

τ B+

1

τ C

632 Half-life

A more commonly used parameter is the half-life Given

a sample of a particular radionuclide the half-life is thetime taken for half the radionuclidersquos atoms to decay Forthe case of one-decay nuclear reactions



64 Example 9

Simulation of many identical atoms undergoing radioactive de-

cay starting with either 4 atoms (left) or 400 (right) Thenumber

at the top indicates how many half-lives have elapsed Note the

law of large numbers with more atoms the overall decay is less

random


minustτ

the half-life is related to the decay constant as follows setN = N 0 2 and t = T ₁₂ to obtain

t12 = ln 2

λ = τ ln 2

This relationship between the half-life and the decayconstant shows that highly radioactive substances arequickly spent while those that radiate weakly endurelonger Half-lives of known radionuclides vary widelyfrom more than 1019 years such as for the very nearlystable nuclide 209Bi to 10minus23 seconds for highly unstable

onesThe factor of ln(2) in the above relations results from thefact that concept of ldquohalf-liferdquo is merely a way of select-

ing a different base other than the natural base e for thelifetime expression The time constant τ is the e minus1 -life the time until only 1e remains about 368 ratherthan the 50 in the half-life of a radionuclide Thus τ islonger than t ₁₂ The following equation can be shown tobe valid

N (t) = N 0 eminustτ = N 0 2minustt12

Since radioactive decay is exponential with a constantprobability each process could as easily be describedwith a different constant time period that (for example)gave its (13)-liferdquo (how long until only 13 is left) or(110)-liferdquo (a time period until only 10 is left) and soon Thus the choice of τ and t12 for marker-times areonly for convenience and from convention They reflecta fundamental principle only in so much as they show that

the same proportion of a given radioactive substance willdecay during any time-period that one chooses

Mathematically the nth life for the above situation wouldbe found in the same way as abovemdashby setting N = N 0 nt = T ₁n and substituting into the decay solution to obtain

t1n = lnnλ

= τ lnn

64 Example

Asampleof 14C has a half-life of 5730 years and a decayrate of 14 disintegration per minute (dpm) per gram ofnatural carbon

If an artifact is found to have radioactivity of 4 dpm pergram of its present C we can find the approximate age ofthe object using the above equation

N = N 0 eminustτ

where N N 0

= 414 asymp 0286

τ = T 12

ln 2 asymp 8267

t = minusτ ln N

N 0asymp 10360

7 Changing decay rates

The radioactive decay modes of electron capture andinternal conversion are known to be slightly sensitive to

chemical and environmental effects that change the elec-tronic structure of the atom which in turn affects thepresence of 1s and 2s electrons that participate in the



10 8 THEORETICAL BASIS OF DECAY PHENOMENA

decay process A small number of mostly light nuclidesare affected For example chemical bonds can affectthe rate of electron capture to a small degree (in gen-eral less than 1) depending on the proximity of elec-trons to the nucleus In 7Be a difference of 09 hasbeen observed between half-lives in metallic and insu-

lating environments[21] This relatively large effect is be-cause beryllium is a small atom whose valence electronsare in 2s atomic orbitals which are subject to electroncapture in 7Be because (like all s atomic orbitals in allatoms) they naturally penetrate into the nucleus

In 1992 Jung et al of theDarmstadt Heavy-IonResearchgroup observed an accelerated β decay of 163Dy66+ Al-though neutral 163Dy is a stable isotope the fully ionized163Dy66+ undergoes β decay into the K and L shells witha half-life of 47 days[22]

Rhenium-187is another spectacular example 187Re nor-

mally beta decays to

187

Os with a half-life of 416 times109 years[23] but studies using fully ionised 187Re atoms(bare nuclei) have found that this can decrease to only33 years This is attributed to bound-state βminus decayof the fully ionised atom ndash the electron is emitted intothe ldquoK-shellrdquo (1s atomic orbital) which cannot occurfor neutral atoms in which all low-lying bound states areoccupied[24]

Decay Rate of Radon-222 as a function of date and time of day

The color-bar gives the power of the observed signal and repre-

sents ~4 seasonal decay rate variation

A number of experiments have found that decay ratesof other modes of artificial and naturally occurring ra-dioisotopes are to a high degree of precision unaffectedby external conditions such as temperature pressure thechemical environment and electric magnetic or gravi-tational fields[25] Comparison of laboratory experimentsover the last century studies of the Oklo natural nuclearreactor (which exemplified the effects of thermal neu-trons on nuclear decay) and astrophysical observationsof the luminosity decays of distant supernovae (which oc-

curred far away so the light has taken a great deal of timeto reach us) for example strongly indicate that unper-turbed decay rates have been constant (at least to within

the limitations of small experimental errors) as a functionof time as well

Recent results suggest the possibility that decay ratesmight have a weak dependence on environmental factorsIt has been suggested that measurements of decay rates of

silicon-32 manganese-54 and radium-226 exhibit smallseasonal variations (of the order of 01)[26][27][28] whilethe decay of Radon-222 exhibit large 4 peak-to-peakseasonal variations[29] proposed to be related to eithersolar flare activity or distance from the Sun Howeversuch measurements are highly susceptible to systematicerrors and a subsequent paper[30] has found no evidencefor such correlations in seven other isotopes (22Na 44Ti108Ag 121Sn 133Ba 241Am 238Pu) and sets upper lim-its on the size of any such effects

8 Theoretical basis of decay phe-nomena

The neutrons and protons that constitute nuclei as wellas other particles that approach close enough to themare governed by several interactions The strong nuclearforce not observed at the familiar macroscopic scale isthe most powerful force over subatomic distances Theelectrostatic force is almost always significant and inthe case of beta decay the weak nuclear force is also in-volved

The interplay of these forces produces a number of dif-ferent phenomena in which energy may be released byrearrangement of particles in the nucleus or else thechange of one type of particle into others These rear-rangements and transformations may be hindered ener-getically so that they do not occur immediately In cer-tain cases random quantum vacuum fluctuations are the-orized to promote relaxation to a lower energy state (theldquodecayrdquo) in a phenomenon known as quantum tunnelingRadioactive decay half-life of nuclides has been mea-suredover timescales of 55 ordersof magnitude from 23x 10minus23 seconds (for hydrogen-7) to 69 x 1031 seconds(for tellurium-128)[31] The limits of these timescales are

set by the sensitivity of instrumentation only and thereare no known natural limits to how brief or long a decayhalf life for radioactive decay of a radionuclide may be

The decay process like all hindered energy transforma-tions may be analogized by a snowfield on a mountainWhile friction between the ice crystals may be supportingthe snowrsquos weight the system is inherently unstable withregard to a state of lower potential energy A disturbancewould thus facilitate the path to a state of greater entropyThe system will move towards the ground state produc-ing heat and the total energy will be distributable overa larger number of quantum states Thus an avalanche

results The total energy does not change in this pro-cess but because of the second law of thermodynam-ics avalanches have only been observed in one direction



11

and that is toward the ground state mdash the state withthe largest number of ways in which the available energycould be distributed

Such a collapse (a decay event ) requires a specificactivation energy For a snow avalanche this energy

comes as a disturbance from outside the system althoughsuch disturbances can be arbitrarily small In the caseof an excited atomic nucleus the arbitrarily small distur-bance comes from quantum vacuum fluctuations A ra-dioactive nucleus (or any excited system in quantum me-chanics) is unstable and can thus spontaneously stabilizeto a less-excited system The resulting transformation al-ters thestructure of thenucleus andresults in theemissionof either a photon or a high-velocity particle that has mass(such as an electron alpha particle or other type)

9 Occurrence and applications

According to the Big Bang theory stable isotopes of thelightest five elements (H He and traces of Li Be andB) were produced very shortly after the emergence of theuniverse in a process called Big Bang nucleosynthesisThese lightest stable nuclides (including deuterium) sur-vive to today but any radioactive isotopes of the light el-ements produced in the Big Bang (such as tritium) havelong since decayed Isotopes of elements heavier thanboron were not produced at all in the Big Bang and thesefirst five elements do not have any long-lived radioiso-

topes Thus all radioactive nuclei are therefore rela-tively young with respect to the birth of the universe hav-ing formed later in various other types of nucleosynthesisin stars (in particular supernovae) and also during on-going interactions between stable isotopes and energeticparticles For example carbon-14 a radioactive nuclidewith a half-life of only 5730 years is constantly pro-duced in Earthrsquos upper atmosphere due to interactions be-tween cosmic rays and nitrogen

Nuclides that are produced by radioactive decay arecalled radiogenic nuclides whether they themselves arestable or not There exist stable radiogenic nuclides that

were formed from short-lived extinct radionuclides in theearly solar system[32][33] The extra presence of these sta-ble radiogenic nuclides (such as Xe-129 from primordialI-129) against the background of primordial stable nu-clides can be inferred by various means

Radioactive decay has been put to use in the techniqueof radioisotopic labeling which is used to track the pas-sage of a chemical substance through a complex system(such as a living organism) A sample of the substance issynthesized with a high concentration of unstable atomsThe presence of the substance in one or another part ofthe system is determined by detecting the locations of de-

cay eventsOn the premise that radioactive decay is truly random(rather than merely chaotic) it has been used in hardware

random-number generators Because the process is notthought to vary significantly in mechanism over time itis also a valuable tool in estimating the absolute ages ofcertain materials For geological materials the radioiso-topes and some of their decay products become trappedwhen a rock solidifies and can then later be used (sub-

ject to many well-known qualifications) to estimate thedate of the solidification These include checking the re-sults of several simultaneous processes and their prod-ucts against each other within the same sample In asimilar fashion and also subject to qualification the rateof formation of carbon-14 in various eras the date offormation of organic matter within a certain period re-lated to the isotopersquos half-life may be estimated becausethe carbon-14 becomes trapped when the organic mat-ter grows and incorporates the new carbon-14 from theair Thereafter the amount of carbon-14 in organic mat-ter decreases according to decay processes that may also

be independently cross-checked by other means (such aschecking the carbon-14 in individual tree rings for ex-ample)

10 Origins of radioactive nuclides

Main article nucleosynthesis

Radioactive primordial nuclides found in the Earth areresidues from ancient supernova explosions which oc-

curred before the formation of the solar system They arethe long-lived fraction of radionuclides surviving in theprimordial solar nebula through planet accretion until thepresent The naturally occurring short-lived radiogenicradionuclides found in rocks are thedaughtersof these ra-dioactive primordial nuclides Another minor source ofnaturally occurring radioactive nuclides are cosmogenicnuclides formed by cosmic ray bombardment of materialin the Earthrsquos atmosphere or crust The radioactive decayof these radionuclides in rocks within Earthrsquos mantle andcrust contribute significantly to Earthrsquos internal heat bud-get

11 Decay chains and multiple

modes

The daughter nuclide of a decay event may also be un-stable (radioactive) In this case it will also decay pro-ducing radiation The resulting second daughter nuclidemay also be radioactive This can lead to a sequence ofseveral decay events Eventually a stable nuclide is pro-duced This is called a decay chain (see this article for

specific details of important natural decay chains)An example is the natural decay chain of 238U which isas follows



12 13 SEE ALSO

Gamma-ray energy spectrum of uranium ore (inset) Gamma-

rays are emitted by decaying nuclides and the gamma-ray energy

can be used to characterize the decay (which nuclide is decaying

to which) Here using the gamma-ray spectrum several nuclides

that are typical of the decay chain of 238U have been identified 226Ra 214Pb 214Bi

bull decays through alpha-emission with a half-life of45 billion years to thorium-234

bull which decays through beta-emission with a half-life of 24 days to protactinium-234

bull which decays through beta-emission with a half-life of 12 minutes to uranium-234

bull which decays through alpha-emission with a half-life of 240 thousand years to thorium-230

bull which decays through alpha-emission with a half-life of 77 thousand years to radium-226

bull which decays through alpha-emission with a half-life of 16 thousand years to radon-222

bull which decays through alpha-emission with a half-life of 38 days to polonium-218

bull which decays through alpha-emission with a half-life of 31 minutes to lead-214

bull which decays through beta-emission with a half-

life of 27 minutes to bismuth-214

bull which decays through beta-emission with a half-life of 20 minutes to polonium-214

bull which decays through alpha-emission with a half-life of 160 microseconds to lead-210

bull which decays through beta-emission with a half-life of 22 years to bismuth-210

bull which decays through beta-emission with a half-life of 5 days to polonium-210

bull which decays through alpha-emission with a half-life of 140 days to lead-206 which is a stable nu-clide

Some radionuclides may have several different paths ofdecay For example approximately 36 of bismuth-212decays through alpha-emission to thallium-208 whileapproximately 64 of bismuth-212 decays throughbeta-emission to polonium-212 Both thallium-208and polonium-212 are radioactive daughter products of

bismuth-212 and both decay directly to stable lead-208

12 Associated hazard warning

signs

bull The trefoil symbol used to indicate ionising radia-tion

bull 2007 ISO radioactivity danger symbol intended forIAEA Category 1 2 and 3 sources defined as dan-gerous sources capable of death or serious injury[1]

bull The dangerous goods transport classification sign forradioactive materials

1 ^ IAEA news release Feb 2007

13 See also

bull Actinides in the environment

bull Background radiation

bull Chernobyl disaster

bull Crimes involving radioactive substances

bull Decay chain

bull Fallout shelter

bull Half-life

bull Lists of nuclear disasters and radioactive incidents

bull National Council on Radiation Protection and Mea-surements

bull Nuclear engineering

bull Nuclear medicine

bull Nuclear pharmacy

bull Nuclear physics

bull Nuclear power

bull Particle decay

bull Poisson process

bull Radiation

bull Radiation therapy



151 Inline 13

bull Radioactive contamination

bull Radioactivity in biology

bull Radiometric dating

bull Radionuclide aka ldquoradio-isotoperdquo

bull Secular equilibrium

bull Transient equilibrium

14 Notes

[1] Radionuclide is the more correct term but radioisotope isalso used The difference between isotope and nuclide isexplained at IsotopeIsotope vs nuclide

15 References

151 Inline

[1] ldquoDecay and Half Liferdquo Retrieved 2009-12-14

[2] Stabin Michael G (2007) ldquo3rdquo Radiation Protec-

tion and Dosimetry An Introduction to Health Physics Springer doi101007978-0-387-49983-3 ISBN 978-0387499826

[3] Best Lara Rodrigues George Velker Vikram (2013)ldquo13rdquo Radiation Oncology Primer and Review Demos

Medical Publishing ISBN 978-1620700044

[4] Loveland W Morrissey D Seaborg GT (2006)Modern Nuclear Chemistry Wiley-Interscience p 57ISBN 0-471-11532-0

[5] Mould Richard F (1995) A century of X-rays and ra-

dioactivity in medicine with emphasis on photographic

records of the early years (Reprint with minor corred) Bristol Inst of Physics Publ p 12 ISBN9780750302241

[6] Kasimir Fajans ldquoRadioactive transformations and the pe-riodic system of the elementsrdquo Berichte der Deutschen

Chemischen Gesellschaft Nr 46 1913 p 422ndash439[7] Frederick Soddy ldquoThe Radio Elements and the Periodic

Lawrdquo Chem News Nr 107 1913 p97ndash99

[8] Sansare K Khanna V Karjodkar F (2011) ldquoEarlyvictims of X-rays a tribute and current percep-tionrdquo Dentomaxillofacial Radiology 40 (2) 123ndash125doi101259dmfr73488299 ISSN 0250-832X PMC3520298 PMID 21239576

[9] Ronald L Kathern and Paul L Ziemer he First FiftyYears of Radiation Protection physicsisuedu

[10] Hrabak M Padovan R S Kralik M Ozretic D

Potocki K (July 2008) ldquoNikola Tesla and the Dis-covery of X-raysrdquo RadioGraphics 28 (4) 1189ndash92doi101148rg284075206 PMID 18635636

[11] Geoff Meggitt (2008) Taming the Rays - A history of

Radiation and Protection Lulucom ISBN 978-1-4092-4667-1

[12] Clarke RH J Valentin (2009) ldquoThe History of ICRPand the Evolution of its Policiesrdquo (PDF) Annals of

the ICRP ICRP Publication 109 39 (1) pp 75ndash110doi101016jicrp200907009 Retrieved 12 May 2012

[13] Rutherford Ernest (6 October 1910) ldquoRadium Standardsand Nomenclaturerdquo Nature 84 (2136) 430ndash431

[14] 10 CFR 201005 US Nuclear Regulatory Commission2009

[15] The Council of the European Communities (1979-12-21)ldquoCouncil Directive 80181EEC of 20 December 1979 onthe approximation of the laws of the Member States relat-ing to Unit of measurement and on the repeal of Directive71354EECrdquo Retrieved 19 May 2012

[16] Radioactive Decay

[17] Patel SB (2000) Nuclear physics an introductionNew Delhi New Age International pp 62ndash72 ISBN9788122401257

[18] Introductory Nuclear Physics KS Krane 1988 JohnWiley amp Sons Inc ISBN 978-0-471-80553-3

[19] Cetnar Jerzy (May 2006) ldquoGeneral solution ofBateman equations for nuclear transmutationsrdquoAnnals of Nuclear Energy 33 (7) 640ndash645doi101016janucene200602004

[20] KS Krane (1988) Introductory Nuclear Physics JohnWiley amp Sons Inc p 164 ISBN 978-0-471-80553-3

[21] Wang B Yan S Limata B et al (2006)ldquoChange of the 7Be electron capture half-life in metal-lic environmentsrdquo The European Physical Journal

A 28 (3) 375ndash377 Bibcode2006EPJA28375Wdoi101140epjai2006-10068-x ISSN 1434-6001

[22] Jung M Bosch F Beckert K et al(1992) ldquoFirst observation of bound-stateβminus decayrdquo Physical Review Letters 69 (15)2164ndash2167 Bibcode1992PhRvL692164Jdoi101103PhysRevLett692164 ISSN 0031-9007

PMID 10046415

[23] Smoliar MI Walker RJ Morgan JW(1996) ldquoRe-Os ages of group IIA IIIA IVAand IVB iron meteoritesrdquo Science 271 (5252)1099ndash1102 Bibcode1996Sci2711099Sdoi101126science27152521099

[24] Bosch F Faestermann T Friese J Heine F KienleP Wefers E Zeitelhack K Beckert K Franzke BKlepper O Kozhuharov C Menzel G MoshammerR Nolden F Reich H Schlitt B Steck M Stoumlh-lker T Winkler T Takahashi K (1996) ldquoObservationof bound-state βndash decay of fully ionized 187Re187Re-187Os Cosmochronometryrdquo Physical Review Letters 77 (26) 5190ndash5193 Bibcode1996PhRvL775190Bdoi101103PhysRevLett775190 PMID 10062738



14 16 EXTERNAL LINKS

[25] Emery GT (1972) ldquoPerturbation of Nu-clear Decay Ratesrdquo (PDF) Annual Review

of Nuclear Science (ACS Publications) 22165ndash202 Bibcode1972ARNPS22165Edoi101146annurevns22120172001121 Retrieved 6August 2012

[26] ldquoThe mystery of varying nuclear decayrdquo Physics World 2 October 2008

[27] Jenkins Jere H Fischbach Ephraim (2009) ldquoPerturba-tion of Nuclear Decay Rates During the Solar Flare of13 December 2006rdquo Astroparticle Physics 31 (6) 407ndash411 arXiv08083156 Bibcode2009APh31407Jdoi101016jastropartphys200904005

[28] Jenkins J H Buncher John B Gruenwald John TKrause Dennis E Mattes Joshua J et al (2009)ldquoEvidence of correlations between nuclear decay ratesand EarthndashSun distancerdquo Astroparticle Physics 32 (1)42ndash46 arXiv08083283 Bibcode2009APh3242J

doi101016jastropartphys200905004

[29] Peter A Sturrock Gideon Steinitz Ephraim FischbachDaniel Javorsek II Jere H Jenkins Analysis of GammaRadiation from a Radon Source Indications of a SolarInfluence Accessed on line September 2 2012

[30] Norman E B Shugart Howard A Joshi Tenzing HFirestone Richard B et al (2009) ldquoEvidence againstcorrelations between nuclear decay rates and EarthndashSundistancerdquo (PDF) Astroparticle Physics 31 (2) 135ndash137 arXiv08103265 Bibcode2009APh31135Ndoi101016jastropartphys200812004

[31] NUBASE evaluation of nuclear and decay properties

[32] Clayton Donald D (1983) Principles of Stellar Evolu-

tion and Nucleosynthesis (2nd ed) University of ChicagoPress p 75 ISBN 0-226-10953-4

[33] Bolt B A Packard R E Price P B (2007) ldquoJohn HReynolds Physics Berkeleyrdquo The University of Califor-nia Berkeley Retrieved 2007-10-01

152 General

bull ldquoRadioactivityrdquo Encyclopaeligdia Britannica 2006

Encyclopaeligdia Britannica Online December 182006

bull Radio-activity by Ernest Rutherford PhdEncyclopaeligdia Britannica Eleventh Edition

16 External links

bull The LundLBNL Nuclear Data Search ndash Containstabulated information on radioactive decay typesand energies

bull Nomenclature of nuclear chemistry

bull Specific activity and related topics

bull The Live Chart of Nuclides ndash IAEA

bull Health Physics Society Public Education Website

bull Beach Chandler B ed (1914) Becquerel RaysThe New Studentrsquos Reference Work Chicago F ECompton and Co

bull Annotated bibliography for radioactivity from theAlsos Digital Library for Nuclear Issues

bull Stochastic Java applet on the decay of radioactiveatoms by Wolfgang Bauer

bull Stochastic Flash simulation on the decay of radioac-tive atoms by David M Harrison

bull ldquoHenri Becquerel The Discovery of Radioactiv-ityrdquo Becquerelrsquos 1896 articles online and analyzedon BibNum [click agrave teacuteleacutecharger for English version]

bull ldquoRadioactive changerdquo Rutherford amp Soddy arti-cle (1903) online and analyzed on Bibnum [click agraveteacuteleacutecharger for English version]



15

17 Text and image sources contributors and licenses

171 Text

bull Radioactive decay Source httpsenwikipediaorgwikiRadioactive_decayoldid=683722344 Contributors The Anome Danny Road-runner Mrwojo Spiff~enwiki Patrick Ahoerstemeier Andrewa LittleDan Kricke Samw Mxn Smack Hike395 HolIgor Chuljin JitseNiesen Audin Furrykef Populus Omegatron Topbanana Pstudier Finlay McWalter PuzzletChung Robbot Romanm Chancemill Se-curiger Merovingian Pengo Giftlite Fudoreaper Netoholic Herbee Everyking Snowdog Curps Eequor Jackol Mmm~enwiki ManuelAnastaacutecio Utcursch Andycjp LiDaobing Antandrus Beland DragonflySixtyseven Icairns GeoGreg Urhixidur Syvanen Olivier De-bre Deglr6328 Kate Running Mike Rosoft Mormegil Freakofnurture Discospinster Rydel Rama Vsmith Mjpieters Mani1 NightGyr Bender235 ESkog Sunborn Tompw El C J-Star Lankiveil Joanjoc~enwiki Hayabusa future RoyBoy Orestes~enwiki GrickBobo192 Stesmo Smalljim Indio~enwiki Cohesion Kjkolb Nsaa Storm Rider Alansohn Mr Adequate AjAldous Seans Potato Busi-ness Ynhockey Velella Harej RainbowOfLight Dirac1933 Sciurinaelig Mikeo DV8 2XL Paraphelion Zntrip Ocollard StradivariusTVDuncanfrance Miss Madeline CharlesC Wdanwatts Jacj Qwertyus Jclemens Scuzzman Martinevos~enwiki Rjwilmsi Jmcc150Nneonneo Bubba73 Watcharakorn Lionelbrits Ground Zero Old Moonraker RexNL Kolbasz Dalef Fresheneesz Guliolopez Gw-ernol Roboto de Ajvol Wavelength Phmer Kymacpherson RussBot Jengelh Shawn81 Kerowren David Woodward Gaius CorneliusCambridgeBayWeather Rsrikanth05 Bovineone Tungsten Grafen Jaxl Welsh ONEder Boy Ino5hiro DJ John Lomn ScottfisherDeadEyeArrow Jeremy Visser Ignitus Wknight94 FF2010 Light current Zzuuzz Sefarkas Closedmouth Јованвб Reyk CharlesH-Bennett CWenger Fourohfour Caco de vidro Moomoomoo Sbyrnes321 DVD R W CIreland Xtraeme Eog1916 Itub MacsBugSmackBot FocalPoint Jclerman Lcarsdata Incnis Mrsi KnowledgeOfSelf Joonhon Hydrogen Iodide NoahWolfe Jmulvey Blue520CMD Beaker Jrockley Yamaguchi Gilliam Carlbunderson TRosenbaum Ati3414 Chris the speller Bluebot Kurykh AgatellerCadmium MK8 Metacomet Uthbrian Reko Sbharris Rogermw NYKevin Cant sleep clown will eat me Ajaxkroon Shalom Yechiel

Abyssal V1adis1av Ioscius KaiserbBot Rrburke VMS Mosaic Rsm99833 Addshore Mrdempsey Megamix Flyguy649 Smooth OXyzzy n Dreadstar -Ozone- Lcarscad Cockneyite Drphilharmonic DMacks Where Bidabadi~enwiki Cyberevil Lambiam Super-Tycoon Sanya JoshuaZ Accurizer Minna Sora no Shita IronGargoyle 16r Ryulong Peyre Squirepants101 Dan Gluck BranStarkPegasus1138 CPM Freelance Intellectual Fdp Tawkerbot2 Chetvorno Bstepp99 ConradIrwin INkubusse Xcentaur RSido VyznevXnebara Nunquam Dormio Solargenerator95 MarsRover Leujohn Smoove Z Myasuda J Tyler Island Dave Quinnculver KanagsGogoDodo HPaul Mad-rick Rracecarr Skittleys Christian75 FastLizard4 Gmoney650 The realavenger Mikewax Thijsbot Epbr123Plmoknijb Dougsim Headbomb Marek69 Deschreiber Davidhorman Meteoritekid FourBlades Stannered Mentifisto AntiVandal-Bot Quintote Jj137 Panu Petteri Houmlglund Hanzoro5 Myanw JAnDbot Arch dude Andonic Xact Snowynight Acroterion GeniacFreedomlinux Bongwarrior VoABot II AuburnPilot Hillgentleman JNW Estonofunciona~enwiki DMcanada Klausok Pixel -) Col-insweet SparrowsWing Indon Animum Dirac66 28421u2232nfenfcenc LorenzoB Tswsl1989 JoergenB Squidonius LewismatsonChuckwatson NatureA16 MartinBot Mermaid from the Baltic Sea Bus stop RnB Leyo Jdelanoy Trusilver Bogey97 Maurice Car-bonaro Cpiral Gzkn Stan J Klimas DarkFalls Dynetrekk~enwiki Tarotcards Pyrospirit Sara0202 Chikinsawsage Fountains of BrynMawr Ohms law Treisijs Jim Swenson Useight Xiahou RJASE1 Idioma-bot ACSE Cuzkatzimhut Malik Shabazz Deor Matt1191VolkovBot ABF VasilievVV Philip Trueman TXiKiBoT Oshwah Xenophrenic Technopat Hqb Jcherbak Someguy1221 Kirkpthomp-son LeaveSleaves Bearian 0x539 Spiral5800 MichaelMorrill Enigmaman Yk Yk Yk Bryan26 Synthebot Falcon8765 Jluo SylentXxxlilbritxxx Insanity Incarnate Kehrbykid Alytkin Borne nocker Brettdog Deconstructhis Starkrm D Recorder Drawde22 SieBot

Tiddly Tom Scarian Viskonsas Caltas Soler97 Keilana Nic92 TJHarrison Oxymoron83 Faradayplank Lightmouse RW MarloeArnobarnard Rj39pooch2 Nergaal Babakathy Martarius ClueBot HujiBot Avenged Eightfold GorillaWarfare Fasettle Bobathon71Pvineet131 The Thing That Should Not Be Plastikspork VsBot Wysprgr2005 Denna Haldane Skaumlpperoumld CounterVandalismBotAkash1209 Dougdp MindstormsKid Jersey emt Opaltehjerkzors Robert Skyhawk Jusdafax Erebus Morgaine Huzzy92 06multanArjayay Radiogenic PhySusie Iohannes Animosus Francisco Albani IXella007 Dekisugi La Pianista Thingg Aitias Jonverve Plas-mic Physics Megachad Party OpusAtrum Johnson-gray MystBot Angerfist~enwiki Thatguyflint Hobbema CalumH93 AmezcackleAddbot Proofreader77 Chorro22 Magus732 Smb6009 Laurinavicius CanadianLinuxUser Leszek Jańczuk WFPM Cst17 Laaknor-Bot PranksterTurtle Exor674 Lordlosss2 Tide rolls Jarble Legobot Luckas-bot Yobot TaBOT-zerem Legobot II Theropod AmbleAyrton Prost Hurricaneguy AnomieBOT DemocraticLuntz Killiondude Jim1138 Piano non troppo AdjustShift Scuzzer Law Mate-rialscientist The High Fin Sperm Whale Citation bot E2eamon Bob Burkhardt LilHelpa Xqbot Transity Capricorn42 RicharddgillWebkinzgirl101 Omnipaedista RibotBOT Amaury Doulos Christos Eugene-elgato Pumpmaster60 FrescoBot Surv1v4l1st Wusel007LucienBOT Wvilhellm Tobby72Pepper Oldlaptop321 MagnaGraecia Footyfanatic3000 HJ Mitchell Cannolis Citationbot 1 ArthreePinethicket Edderso 10metreh Odyssey xg A8UDI Minivip Meaghan Double sharp TobeBot Trappist the monk Lotje NdkartikTheBFG Mozi17 Comet Tuttle Mathgeek31415926 Dinamik-bot Vrenator Tobias1984 Bluefist Specs112 SilverbladeGR Cfs-gfds Fastilysock Cutelyaware Sampathsris Minimac TjBot TomBeasley KuanRyan Androstachys Alison22 DASHBot TGCP Bot-deSki John of Reading WikitanvirBot Lunaibis RedHab ScottyBerg Yt95 RenamedUser01302013 Kulmeetster Wikipelli K6kaSydneyanders JSquish ZeacuteroBot John Cline PBS-AWB Mkevinjnr Suslindisambiguator Elio96 Gz33 QEDK Aschwole L Kens-ington MonoAV Maschen Donner60 Scientific29 ChuispastonBot RockMagnetist Ryan Pianesi Newtrend19 Petrb ClueBot NGCrazyman121 Littleal38 Verpies Satellizer Baseball Watcher Slartibartfastibast Widr Dasetwundabal Oddbodz Helpful Pixie BotCiro612 Strike Eagle Calabe1992 Bibcode Bot Jeraphine Gryphon BG19bot Teiu88 Northamerica1000 Wiki13 ElphiBot MusikAn-imal Cynaide Shampa1 Flying hippo705 Glevum DynamicDino Adebish Zedshort Hamish59 Mgoelzer SfHuIcTk ThegreatgrabberAchowat Imawesome12345678910 ArrakisFrance 555snowy Kisokj Ezekiel25q Wolf11235 Cyprien1997 BrightStarSky Apples122Ultimatewikimaster12345 Reatlas Joeinwiki Cavisson Tentinator Awesome boss 69 69 Bond064 Jyotmankad CloudStrifeNBHMJwratner1 Applezpi3 Genome0514 StevenD99 Bkilli1 Ilikethemchickenwing$ AndthewinnerisCole Zane7777 Shbew MonkbotUDDM Vieque Thenapster1426 TheFireRises Micbattle064 Paul2lyfe Amortias Pacifist peeta Radioactiveisreallyawesome Kaspar-Bot Cerberus123 Never gonna See me Lexi sioz Subhajit07 Soumik Pattanayak Bigdaddyyyyy69 and Anonymous 805

172 Images

bull FileAlfa_beta_gamma_radiationsvg Source httpsuploadwikimediaorgwikipediacommonsdd6Alfa_beta_gamma_radiation

svg License CC BY 25 Contributors Traced from this PNG image Original artist UserStanneredbull FileAlpha_Decaysvg Source httpsuploadwikimediaorgwikipediacommons779Alpha_Decaysvg License Public domain Con-

tributors This vector image was created with Inkscape Original artist Inductiveload



16 17 TEXT AND IMAGE SOURCES CONTRIBUTORS AND LICENSES

bull FileAmbox_importantsvg Source httpsuploadwikimediaorgwikipediacommonsbb4Ambox_importantsvg License Public do-main Contributors Own work based off of ImageAmbox scalessvg Original artist Dsmurat (talk middot contribs)

bull FileCrookes_tube_xray_experimentjpg Source httpsuploadwikimediaorgwikipediacommons110Crookes_tube_xray_experimentjpg License Public domain Contributors Downloaded 2007-12-23 from lta data-x-rel=nofollow class=external texthref=httpbooksgooglecombooksid=whc4AAAAMAAJltspangtampltspangtpg=PT5gtWilliam J Morton and Edwin W Hammer(1896) The X-ray or Photography of the Invisible and its value in Surgery American Technical Book Co New York fig 54ltagt onGoogle Books Original artist William J Morton

bull FileDecayRate_vs_Solar_Timepng Source httpsuploadwikimediaorgwikipediacommonsdd3DecayRate_vs_Solar_TimepngLicense Public domain Contributors Original artist

bull FileGammaspektrum_UranerzjpgSource https uploadwikimediaorgwikipediacommons88cGammaspektrum_Uranerzjpg Li-

cense CC BY-SA 30 Contributors Own work Original artist Wusel007

bull FileHalflife-simgif Source httpsuploadwikimediaorgwikipediacommons33fHalflife-simgif License Public domain Contribu-

tors Own work Original artist Sbyrnes321

bull FileNuclearReactionpng Source httpsuploadwikimediaorgwikipediacommons77dNuclearReactionpng License CC BY-SA30 Contributors Own work Original artist Michalsmid

bull FilePeriodic_Table_Stability_amp_Radioactivitypng Source httpsuploadwikimediaorgwikipediacommonscc4Periodic_Table_Stability_26_Radioactivitypng License CC BY-SA 25 Contributors httpscommonswikimediaorgwikiFilePeriodic_Table_Radioactivitysvg Original artist Alessio Rolleri (et al) Lexi sioz

bull FilePierre_and_Marie_Curiejpg Source httpsuploadwikimediaorgwikipediacommons66cPierre_and_Marie_Curiejpg Li-

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2 2 EARLY HEALTH DANGERS

cosmic rays Radionuclides may also be produced artifi-cially in particle accelerators or nuclear reactors resultingin 650 of these with half-lives of over an hour and sev-eral thousand more with even shorter half-lives See thislist of nuclides for a list of these sorted by half life

1 History of discovery

Pierre and Marie Curie in their Paris laboratory before 1907

Radioactivity was discovered in 1896 by the Frenchscientist Henri Becquerel while working withphosphorescent materials[5] These materials glow

in the dark after exposure to light and he suspectedthat the glow produced in cathode ray tubes by X-raysmight be associated with phosphorescence He wrappeda photographic plate in black paper and placed variousphosphorescent salts on it All results were negativeuntil he used uranium salts The uranium salts causeda blackening of the plate in spite of the plate beingwrapped in black paper These radiations were given thename ldquoBecquerel Raysrdquo

It soon became clear that the blackening of the plate hadnothing to do with phosphorescence as the blackeningwas also produced by non-phosphorescent salts of ura-

nium and metallic uranium It became clear from theseexperiments that there was a form of invisible radiationthat could pass through paper and was causing the plateto react as if exposed to light

At first it seemed as though the new radiation was sim-ilar to the then recently discovered X-rays Further re-search by Becquerel Ernest Rutherford Paul VillardPierre Curie Marie Curie and others showed that thisform of radioactivity was significantly more complicatedRutherford was the first to realize that all such elementsdecay in accordance with the same mathematical expo-nential formula Rutherford and his student Frederick

Soddy were the first to realize that many decay processesresulted in the transmutation of one element to anotherSubsequently the radioactive displacement law of Fajans

and Soddy was formulated to describe the products ofalpha and beta decay[6][7]

The early researchers also discovered that many otherchemical elements besides uranium have radioactiveisotopes A systematic search for the total radioactivity

in uranium ores also guided Pierre and Marie Curie toisolate two new elements polonium and radium Exceptfor the radioactivity of radium the chemical similarityof radium to barium made these two elements difficult todistinguish

2 Early health dangers

Main article ionizing radiationThedangers of ionizing radiationdue to radioactivity and

Taking an X-ray image with early Crookes tube apparatus in

1896 The Crookes tube is visible in the centre The standingman is viewing his hand with a fluoroscope screen this was a

common way of setting up the tube No precautions against ra-

diation exposure are being taken its hazards were not known at

the time

X-rays were not immediately recognized

21 X-rays

The discovery of x‑rays by Wilhelm Roumlntgen in 1895 ledto widespread experimentation by scientists physicians

and inventors Many people began recounting stories ofburns hair loss and worse in technical journals as earlyas 1896 In February of that year Professor Daniel andDr Dudley of Vanderbilt University performed an ex-periment involving X-raying Dudleyrsquos head that resultedin his hair loss A report by Dr HD Hawks of his suf-fering severe hand and chest burns in an X-ray demon-stration was the first of many other reports in Electrical

Review[8]

Other experimenters including Elihu Thomson andNikola Tesla also reported burns Thomson deliberatelyexposed a finger to an X-ray tube over a period of time

and suffered pain swelling and blistering[9] Other ef-fects including ultraviolet rays and ozone were some-times blamed for the damage[10] and many physicians



3













much less



















4 4 TYPES OF DECAY


4 Types of decay

α

β

γ




layer of lead





N

Z

Parent

atom

α

β minus

n

p

β +EC









5



























Constant quantities



cay rate










t12 = ln(2)

λ = τ ln(2)

A = minusdN dt

= λN

S Aa0 = minusdN dt

t=0

= λN 0



cay














minusdN dt prop N





minustτ






N A = N A0eminusλt




1048617


is[17]


N


Chain of two decays





dN Bdt







N B = N A0λA

λB minus λA


1048617


limλBrarr0



1048617983133 = N A0λA

0 minus λA


1048617 = N A0

10486161








dN jdt





N = N A + N B + N C


dN Adt

= minus

983080dN B

dt +

dN C dt

983081



λ = λB + λC

Notice that

dN Adt

lt 0 dN B

dt gt 0

dN C dt

gt 0


N A = N A0eminusλt



N B = λB

λ N A0


1048617

N C = λC

λ












minustτ




τ = 1

λ


λ = λB + λC


1

τ = λ = λB + λC =

1

τ B+

1

τ C

632 Half-life





64 Example 9





random


minustτ


t12 = ln 2

λ = τ ln 2








t1n = lnnλ

= τ lnn

64 Example



N = N 0 eminustτ

where N N 0

= 414 asymp 0286

τ = T 12

ln 2 asymp 8267

t = minusτ ln N

N 0asymp 10360












187


















11



















modes





12 13 SEE ALSO
























signs





13 See also





bull Decay chain


bull Half-life







bull Nuclear power

bull Particle decay


bull Radiation




151 Inline 13







14 Notes


15 References

151 Inline
































PMID 10046415


















152 General




16 External links














15


171 Text




172 Images






























173 Content license




3













much less



















4 4 TYPES OF DECAY


4 Types of decay

α

β

γ




layer of lead





N

Z

Parent

atom

α

β minus

n

p

β +EC









5



























Constant quantities



cay rate










t12 = ln(2)

λ = τ ln(2)

A = minusdN dt

= λN

S Aa0 = minusdN dt

t=0

= λN 0



cay














minusdN dt prop N





minustτ






N A = N A0eminusλt




1048617


is[17]


N


Chain of two decays





dN Bdt







N B = N A0λA

λB minus λA


1048617


limλBrarr0



1048617983133 = N A0λA

0 minus λA


1048617 = N A0

10486161








dN jdt





N = N A + N B + N C


dN Adt

= minus

983080dN B

dt +

dN C dt

983081



λ = λB + λC

Notice that

dN Adt

lt 0 dN B

dt gt 0

dN C dt

gt 0


N A = N A0eminusλt



N B = λB

λ N A0


1048617

N C = λC

λ












minustτ




τ = 1

λ


λ = λB + λC


1

τ = λ = λB + λC =

1

τ B+

1

τ C

632 Half-life





64 Example 9





random


minustτ


t12 = ln 2

λ = τ ln 2








t1n = lnnλ

= τ lnn

64 Example



N = N 0 eminustτ

where N N 0

= 414 asymp 0286

τ = T 12

ln 2 asymp 8267

t = minusτ ln N

N 0asymp 10360












187


















11



















modes





12 13 SEE ALSO
























signs





13 See also





bull Decay chain


bull Half-life







bull Nuclear power

bull Particle decay


bull Radiation




151 Inline 13







14 Notes


15 References

151 Inline
































PMID 10046415


















152 General




16 External links














15


171 Text




172 Images






























173 Content license




4 4 TYPES OF DECAY


4 Types of decay

α

β

γ




layer of lead





N

Z

Parent

atom

α

β minus

n

p

β +EC









5



























Constant quantities



cay rate










t12 = ln(2)

λ = τ ln(2)

A = minusdN dt

= λN

S Aa0 = minusdN dt

t=0

= λN 0



cay














minusdN dt prop N





minustτ






N A = N A0eminusλt




1048617


is[17]


N


Chain of two decays





dN Bdt







N B = N A0λA

λB minus λA


1048617


limλBrarr0



1048617983133 = N A0λA

0 minus λA


1048617 = N A0

10486161








dN jdt





N = N A + N B + N C


dN Adt

= minus

983080dN B

dt +

dN C dt

983081



λ = λB + λC

Notice that

dN Adt

lt 0 dN B

dt gt 0

dN C dt

gt 0


N A = N A0eminusλt



N B = λB

λ N A0


1048617

N C = λC

λ












minustτ




τ = 1

λ


λ = λB + λC


1

τ = λ = λB + λC =

1

τ B+

1

τ C

632 Half-life





64 Example 9





random


minustτ


t12 = ln 2

λ = τ ln 2








t1n = lnnλ

= τ lnn

64 Example



N = N 0 eminustτ

where N N 0

= 414 asymp 0286

τ = T 12

ln 2 asymp 8267

t = minusτ ln N

N 0asymp 10360












187


















11



















modes





12 13 SEE ALSO
























signs





13 See also





bull Decay chain


bull Half-life







bull Nuclear power

bull Particle decay


bull Radiation




151 Inline 13







14 Notes


15 References

151 Inline
































PMID 10046415


















152 General




16 External links














15


171 Text




172 Images






























173 Content license




5



























Constant quantities



cay rate










t12 = ln(2)

λ = τ ln(2)

A = minusdN dt

= λN

S Aa0 = minusdN dt

t=0

= λN 0



cay














minusdN dt prop N





minustτ






N A = N A0eminusλt




1048617


is[17]


N


Chain of two decays





dN Bdt







N B = N A0λA

λB minus λA


1048617


limλBrarr0



1048617983133 = N A0λA

0 minus λA


1048617 = N A0

10486161








dN jdt





N = N A + N B + N C


dN Adt

= minus

983080dN B

dt +

dN C dt

983081



λ = λB + λC

Notice that

dN Adt

lt 0 dN B

dt gt 0

dN C dt

gt 0


N A = N A0eminusλt



N B = λB

λ N A0


1048617

N C = λC

λ












minustτ




τ = 1

λ


λ = λB + λC


1

τ = λ = λB + λC =

1

τ B+

1

τ C

632 Half-life





64 Example 9





random


minustτ


t12 = ln 2

λ = τ ln 2








t1n = lnnλ

= τ lnn

64 Example



N = N 0 eminustτ

where N N 0

= 414 asymp 0286

τ = T 12

ln 2 asymp 8267

t = minusτ ln N

N 0asymp 10360












187


















11



















modes





12 13 SEE ALSO
























signs





13 See also





bull Decay chain


bull Half-life







bull Nuclear power

bull Particle decay


bull Radiation




151 Inline 13







14 Notes


15 References

151 Inline
































PMID 10046415


















152 General




16 External links














15


171 Text




172 Images






























173 Content license











Constant quantities



cay rate










t12 = ln(2)

λ = τ ln(2)

A = minusdN dt

= λN

S Aa0 = minusdN dt

t=0

= λN 0



cay














minusdN dt prop N





minustτ






N A = N A0eminusλt




1048617


is[17]


N


Chain of two decays





dN Bdt







N B = N A0λA

λB minus λA


1048617


limλBrarr0



1048617983133 = N A0λA

0 minus λA


1048617 = N A0

10486161








dN jdt





N = N A + N B + N C


dN Adt

= minus

983080dN B

dt +

dN C dt

983081



λ = λB + λC

Notice that

dN Adt

lt 0 dN B

dt gt 0

dN C dt

gt 0


N A = N A0eminusλt



N B = λB

λ N A0


1048617

N C = λC

λ












minustτ




τ = 1

λ


λ = λB + λC


1

τ = λ = λB + λC =

1

τ B+

1

τ C

632 Half-life





64 Example 9





random


minustτ


t12 = ln 2

λ = τ ln 2








t1n = lnnλ

= τ lnn

64 Example



N = N 0 eminustτ

where N N 0

= 414 asymp 0286

τ = T 12

ln 2 asymp 8267

t = minusτ ln N

N 0asymp 10360












187


















11



















modes





12 13 SEE ALSO
























signs





13 See also





bull Decay chain


bull Half-life







bull Nuclear power

bull Particle decay


bull Radiation




151 Inline 13







14 Notes


15 References

151 Inline
































PMID 10046415


















152 General




16 External links














15


171 Text




172 Images






























173 Content license







minusdN dt prop N





minustτ






N A = N A0eminusλt




1048617


is[17]


N


Chain of two decays





dN Bdt







N B = N A0λA

λB minus λA


1048617


limλBrarr0



1048617983133 = N A0λA

0 minus λA


1048617 = N A0

10486161








dN jdt





N = N A + N B + N C


dN Adt

= minus

983080dN B

dt +

dN C dt

983081



λ = λB + λC

Notice that

dN Adt

lt 0 dN B

dt gt 0

dN C dt

gt 0


N A = N A0eminusλt



N B = λB

λ N A0


1048617

N C = λC

λ












minustτ




τ = 1

λ


λ = λB + λC


1

τ = λ = λB + λC =

1

τ B+

1

τ C

632 Half-life





64 Example 9





random


minustτ


t12 = ln 2

λ = τ ln 2








t1n = lnnλ

= τ lnn

64 Example



N = N 0 eminustτ

where N N 0

= 414 asymp 0286

τ = T 12

ln 2 asymp 8267

t = minusτ ln N

N 0asymp 10360












187


















11



















modes





12 13 SEE ALSO
























signs





13 See also





bull Decay chain


bull Half-life







bull Nuclear power

bull Particle decay


bull Radiation




151 Inline 13







14 Notes


15 References

151 Inline
































PMID 10046415


















152 General




16 External links














15


171 Text




172 Images






























173 Content license





dN jdt





N = N A + N B + N C


dN Adt

= minus

983080dN B

dt +

dN C dt

983081



λ = λB + λC

Notice that

dN Adt

lt 0 dN B

dt gt 0

dN C dt

gt 0


N A = N A0eminusλt



N B = λB

λ N A0


1048617

N C = λC

λ












minustτ




τ = 1

λ


λ = λB + λC


1

τ = λ = λB + λC =

1

τ B+

1

τ C

632 Half-life





64 Example 9





random


minustτ


t12 = ln 2

λ = τ ln 2








t1n = lnnλ

= τ lnn

64 Example



N = N 0 eminustτ

where N N 0

= 414 asymp 0286

τ = T 12

ln 2 asymp 8267

t = minusτ ln N

N 0asymp 10360












187


















11



















modes





12 13 SEE ALSO
























signs





13 See also





bull Decay chain


bull Half-life







bull Nuclear power

bull Particle decay


bull Radiation




151 Inline 13







14 Notes


15 References

151 Inline
































PMID 10046415


















152 General




16 External links














15


171 Text




172 Images






























173 Content license




64 Example 9





random


minustτ


t12 = ln 2

λ = τ ln 2








t1n = lnnλ

= τ lnn

64 Example



N = N 0 eminustτ

where N N 0

= 414 asymp 0286

τ = T 12

ln 2 asymp 8267

t = minusτ ln N

N 0asymp 10360












187


















11



















modes





12 13 SEE ALSO
























signs





13 See also





bull Decay chain


bull Half-life







bull Nuclear power

bull Particle decay


bull Radiation




151 Inline 13







14 Notes


15 References

151 Inline
































PMID 10046415


















152 General




16 External links














15


171 Text




172 Images






























173 Content license










187


















11



















modes





12 13 SEE ALSO
























signs





13 See also





bull Decay chain


bull Half-life







bull Nuclear power

bull Particle decay


bull Radiation




151 Inline 13







14 Notes


15 References

151 Inline
































PMID 10046415


















152 General




16 External links














15


171 Text




172 Images






























173 Content license




11



















modes





12 13 SEE ALSO
























signs





13 See also





bull Decay chain


bull Half-life







bull Nuclear power

bull Particle decay


bull Radiation




151 Inline 13







14 Notes


15 References

151 Inline
































PMID 10046415


















152 General




16 External links














15


171 Text




172 Images






























173 Content license




12 13 SEE ALSO
























signs





13 See also





bull Decay chain


bull Half-life







bull Nuclear power

bull Particle decay


bull Radiation




151 Inline 13







14 Notes


15 References

151 Inline
































PMID 10046415


















152 General




16 External links














15


171 Text




172 Images






























173 Content license




151 Inline 13







14 Notes


15 References

151 Inline
































PMID 10046415


















152 General




16 External links














15


171 Text




172 Images






























173 Content license

















152 General




16 External links














15


171 Text




172 Images






























173 Content license




15


171 Text




172 Images






























173 Content license




























173 Content license


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