RadioactivitySpontaneous emission of radiation from the nucleus of an unstable isotope.
Marie Curie1867 - 1934
Wilhelm Roentgen1845 - 1923
X-Rays
emitted
by cathode
ray tube
Poloniu
m and
radium
Antoine Henri Becquerel1852 - 1908
Uranium
produced
X-rays
Nucleus = Protons+ Neutrons
nucleons
A = nucleon number (atomic mass number)Gives you mass density of element
Z = proton number (atomic number) Gives chemical properties (and name)
N = neutron number
A=N+Z
Nuclear Physics
Li63
A
Z
Periodic_Table
A material is known to be an isotope of lead. Which of the following can be specified?
1. The atomic mass number
2. The neutron number
3. The number of protons
A material is known to be an isotope of lead. Which of the following can be specified?
1 2 3
0% 0%0%
1. The atomic mass number
2. The neutron number
3. The number of protons
Lead Z=82
Chemical properties (and name) determined by number of protons (Z)
But protons repel one another (Coulomb Force) and when Z is large it becomes harder to put more protons into a nucleus without adding even more neutrons to provide more of the Strong Force. For this reason, in heavier nuclei N>Z.
# protons = # neutrons
Where does the energy released in the nuclear reactions of the sun come from?
1 2 3
0% 0%0%
1. covalent bonds between atoms
2. binding energy of electrons to the nucleus
3. binding energy of nucleons
Where does the energy released in the nuclear reactions of the sun come from?
1 2 3
0% 0%0%
1. covalent bonds between atoms
2. binding energy of electrons to the nucleus
3. binding energy of nucleons
Strong Nuclear Force
• Acts on Protons and Neutrons
• Strong enough to overcome Coulomb repulsion
• Acts over very short distancesTwo atoms don’t feel force
Hydrogen atom: Binding energy =13.6eV
Binding energy of deuteron = or 2.2Mev! That’s around 200,000 times bigger!
2.2106eV
Simplest Nucleus: Deuteron=neutron+protonneutron proton
Very strong force
Coulomb force
electron
proton
Strong Nuclear Force
(of electron to nucleus)
Binding Energy
Einstein’s famous equation E = m c2
Proton: mc2 = 938.3MeV
Neutron: mc2= 939.5MeV
Deuteron: mc2 =1875.6MeV
Adding these, get 1877.8MeV
Difference is Binding energy, 2.2MeV
MDeuteron = MProton + MNeutron – |Binding Energy|
Iron (Fe) has the most binding energy/nucleon. Lighter have too few nucleons, heavier have too many.
BIN
DIN
G E
NER
GY
in M
eV/n
ucle
on
92238U
10
Binding Energy Plot
Fission
Fusio
n Fusion = Combining small atoms into largeFission = Breaking large atoms into small
E = mc2
• Mass can be converted to energy• Energy can be converted to mass• Mass and energy are the same thing• The total amount of mass plus energy in the universe is constant
Mass Defect in Fission
• When a heavy element (one beyond Fe) fissions, the resulting products have a combined mass which is less than that of the original nucleus.
Mass Defect of Alpha ParticleMass Defect of Alpha Particle
Mass difference = 0.0304 u
Binding energy = 28.3 MeV
Fusion product has less mass than the sum of the parts.
Which of the following is most correct for the total binding energy of an Iron atom (Z=26)?
1 2 3 4
0% 0%0%0%
1. 9 MeV2. 234 MeV3. 270 MeV4. 504 Mev
BIN
DIN
G E
NER
GY
in M
eV/n
ucle
on
Which of the following is most correct for the total binding energy of an Iron atom (Z=26)?
1 2 3 4
0% 0%0%0%
1. 9 MeV2. 234 MeV3. 270 MeV4. 504 Mev
Total B.E 56x9=504 MeV
BIN
DIN
G E
NER
GY
in M
eV/n
ucle
on
For Fe, B.E./nucleon 9MeV
2656Fe has 56 nucleons
particles: nucleii 24He
particles: electrons
: photons (more energetic than x-rays) penetrate!
3 Types of Radioactivity
Easily Stopped
Stopped by metal
Radioactive sources
B field into screen
detector
Alpha Decay
• Alpha decay occurs when there are too many protons in the nucleus which cause excessive electrostatic repulsion.
• An alpha particle is ejected from the nucleus.• An alpha particle is 2 protons and 2 neutrons.• An alpha particle is also a helium nucleus.• Alpha particle symbol:
42He
Beta Decay• Beta decay occurs when neutron to proton ratio is
too big• A neutron is turned into a proton and electron and
an antineutrino• The electron and the antineutrino are emitted
Gamma Decay• Gamma decay occurs when the nucleus is at too high an energy• Nucleus falls down to a lower energy level• High energy photon – gamma ray - is emitted
92238U 90
234Th: example 24He recall
: example
Decay Rules1) Nucleon Number is conserved.2) Atomic Number (charge) is conserved.3) Energy and momentum are conserved.
: example 00
* PP AZ
AZ
1) 238 = 234 + 4 Nucleon number conserved2) 92 = 90 + 2 Charge conserved
e01
11
10 pn
Needed to conserve energy and momentum.
00
A nucleus undergoes decay. Which of the following is FALSE?
1 2 3
0% 0%0%
1. Nucleon number decreases by 4 2. Neutron number decreases by 2 3. Charge on nucleus increases by 2
A nucleus undergoes decay. Which of the following is FALSE?
1 2 3
0% 0%0%
1. Nucleon number decreases by 4 2. Neutron number decreases by 2 3. Charge on nucleus increases by 2
decay is the emission of 24He
He42
23490
23892 ThU
Z decreases by 2(charge decreases!)
A decreases by 4
The nucleus undergoes decay. Which of the following is true?
1 2
0%0%
90234Th
1. The number of protons in the daughter nucleus increases by one.
2. The number of neutrons in the daughter nucleus increases by one.
decay involves emission of an electron: creation of a charge -e.
In fact, inside the nucleus, and the electron and neutrino “escape.”
n p e e
00
01
23491
23490 PaTh
e
Radioactive Decay
23892U 4
2He 23490 Th
23490Th 0
1e 23491Pa
4.5 x 109 yr half-life
24 day half-life1.17 min half-life
23491Pa
01e 234
92 U250,000 yr half-life
Nuclear Decay Links
• http://physics.bu.edu/cc104/uudecay.html• http://www.physics.umd.edu/lecdem/honr22
8q/notes/U238scheme.gif• http://www.physics.umd.edu/lecdem/honr22
8q/notes/fourdecschemes.gif
Which of the following decays is NOT allowed?
1 2 3 4 5
0% 0% 0%0%0%
92238U 90
234Th
HePbPo 42
21082
21484
00
01
4020
4019 pK
e
NC 147
146
1. 2. 3. 4.
Which of the following decays is NOT allowed?
1 2 3 4 5
0% 0% 0%0%0%
92238U 90
234Th
HePbPo 42
21082
21484
00
01
4020
4019 pK
e
NC 147
146
1. 2. 3. 4.
238 = 234 + 492 = 90 + 2
214 = 210 + 4
84 = 82 + 2
14 = 14+0
6 <> 7+0
40 = 40+0+019 = 20-1+0
Decays per second, or “activity”:If the number of radioactive nuclei present is cut in half, how does the activity change?
1 2 3
0% 0%0%
Nt
NNo. of nuclei present
decay constant
1. It remains the same
2. It is cut in half 3. It doubles
Decays per second, or “activity”Start with 16 14C atoms.After 6000 years, there are only 8 left.How many will be left after another 6000 years?
1 2 3
0% 0%0%
Nt
N No. of nuclei present
decay constant
Every 6000 years ½ of atoms decay
1. 02. 43. 6
Instead of base e we can use base 2:
N(t)N0e tSurvival:
No. of nuclei present at time t
No. we started with at t=0
e t 2
tT1/2
T1/2
0.693
where
Then we can write N(t)N0e t N0 2
t
T1/2
Half life
Radioactivity Quantitatively
Nt
N
No. of nuclei present
decay constant
Decays per second, or “activity”
Carbon Dating• Cosmic rays cause transmutation of Nitrogen to Carbon-14
• C-14 is radioactive with a half-life of 5730 years– It decays back to Nitrogen by beta decay
• The ratio of C-12 (stable) atoms to C-14 atoms in our atmosphere is fairly constant – about 1012/1
• This ratio is the same in living things that obtain their carbon from the atmosphere
1 14 1 140 7 1 6n N H C
14 0 146 1 7C e N
You are radioactive!
One in 8.3x1011 carbon atoms is 14C which decays with a ½ life of 5730 years. Determine # of decays/gram of Carbon.
Nt
N
11
2314 103.8
11002.6
mole12
0.1g
N
2/1
693.T
1-12s1083.36060243655730
693.
gatoms
106 10
decays/s 23.0
Carbon DatingWe just determined that living organisms should have a decay rate of about 0.23 decays/ gram of carbon.
The bones of an ice man are found to have a decay rate of 0.115 decays/gram. We can estimate he died about 6000 years ago.
Summary• Nuclear Reactions– Nucleon number conserved– Charge conserved– Energy/Momentum conserved– particles = nuclei– - particles = electrons– particles = high-energy photons
• Decays– Half-Life is time for ½ of atoms to decay
N(t)N0e tSurvival:
T1/2
0.693
24He
How Stuff Works Site
• Visit the How Stuff Works Site to learn more details about nuclear energy