Half-life – length of time it takes for a radioactive substance to decay to half its original mass

As a radioactive substance decays, there’ll be less and less of the radioactive substance remaining, while more of the new substance will form. There will come a time during the decay process when exactly half of the original mass of the radioactive substance remains unchanged. The time it takes for the substance to decay to half of its original mass is described as the half-life of the substance.

3 days of decaying •Decaying of a radioactive substance is at a constant rate•Temperature, pressure, and amount do not change the half-life of a substance•Each radioisotope has its own half-life

10 g5 g new

5 g old

Number of half-life period is the number of times a radioactive substance decays in half to go from one mass to another.

Original mass Remaining mass16 g 1 half life> 8 g 2nd half life> 4 g 3rd half life> 2 g

A.If the original mass and the remaining mass are known in a question:Use arrows to represent one half-life period

How many half-life periods does it takes for a radioactive substance to decay from the original mass of 12 grams to the remaining mass of 0.75 g12 6 3 1.5 0.75 Count the arrows – 4 half-lives

B. If the length of time and the half-life are known in a question:

Use the equation # of half-life periods = length of timehalf-life

The half-life of a radioisotope is 15 minutes. In 75 minutes, how many half-life periods would the substance have gone through?

Known half-life = 15 minuteslength of time = 75 minutes

# of half-life periods = 75 = 515

Length of time of decayA.If the half-life and the number of half-life periods are given in a questionLength of time = half-life x number of half-life periods

Approximately how long will it take for a radioactive42K to undergo 6 half-life periods?

Known half-life from Table N = 12.4 hours# of half-life periods = 6

Length of time = 12.4 hours x 6 = 74.4 hours

B. If half-life, original mass and remaining mass are known

How long will it take for K-42 to decay from 100 grams to 12.5 grams?

Known original mass = 100 gramsremaining mass = 12.5 gramshalf-life of K-42 = 12.4 hours

100 g 50 g 25 g 12.5 g 3 half-life periods

Length of time = 12.5 hours x 3 = 37.2 hours

Half-lifeA.If length of time and number of half-life periods are given in a question

Half-life = length of time half-life period

What is the half-life of an unknown radioisotope if it takes 12 years for the radioisotope to undergo 5 half-life periods?

Known length of time = 12 yearshalf-life periods = 5

Half-life = 12 = 2.4 years 5

B. If the length of time, original mass and remaining mass are given in a question

An unknown substance decays from 64 grams to 2 grams in 1.5 x 103 years. What is the half-life of this substance?

Known original mass = 64 gramsremaining mass = 2 gramslength of time = 1.5 x 103 years

64 32 g 16 g 8 4 g 2 g 5 half-lives

Half-life = 1500 = 300 years 5

Determining original mass of a substanceA.If the number of half life periods and the remaining mass are given in an equation

After 6 half-life periods, 15 grams of an unknown radioisotope remains. What was the original mass of the unknown radioisotope?

Known remaining mass = 15 g# half-life periods = 6

960 g 480 g 240 g 120 g 60 g 30 g 15 gOriginal mass = 960 g

B. If the length of time, half-life and remaining mass are given in a question

After 24 days of decaying, a 5 gram sample of 131I remains unchanged. What amount of the 131I was present at the beginning of the decay?

Known remaining mass = 5 glength of time = 24 dayshalf-life = 8.07 days

# of half-life periods = 24 = 38.07

40 g 20 g 10 g 5 gOriginal mass = 40 g

Remaining MassA.If the number of half life periods and the original mass are given in a question

After 4 half-life periods, how many grams of a 12 mg sample f a radioisotope will remain unchanged?

Known original mass = 12 mg# half-life periods = 4

12 6 3 1.5 0.75 mg remain

B. If the length of time, half-life and original mass are known in a question

In approximately 8 x 103 years, how many grams of a 100 gram sample of radon-226 will remain unchanged?

Known original mass = 100 glength of time = 8 x 103 yearshalf-life = 1.6 x 103 years

# of half-life periods = 8000 = 51600

100 50 25 12.5 6.25 3.125 g remain

Fraction remainingA.If the number of half-life periods of decaying are given in a question

Fraction remaining = 1 n = number of half-life periods 2n

What fraction of Au-198 will remain unchanged after 4 half-life periods?

Fraction remaining = 1 = 1 24 16

B. If length of time and half-life of a substance are given in a question

Fraction remaining = 1 t = length of time 2t/T T = half-life

What fraction of Ne-19 will remain unchanged after 86 seconds?

Known length of time = 86 sechalf-life = 17.2 sec

Fraction remaining = 1 = 1 = 1 286/17.2 25 32

Using fraction remaining and length of time to determine isotope symbol

What radioisotope will have 1/16th of its original mass remaining after about 112 years?

Known fraction remaining = 1/16length of time = 112 years

1/16 = 1/2n where n = 4

4 = 112/half-lifeHalf-life = 28 years

On table N – Sr-90 has a half-life of 28.1 years.

To identify which isotopedecays to the greatest extent in a given time periodLOOK for the radioisotope with the shortest half-life

decays to the least extent in a given time periodLOOK for the radioisotope with the longest half-life

To determine which radioactive sample hasgreatest amount remaining after a given periodLOOK for radioisotope with LONGEST half-life and

MOST mass

least amount remaining after a given periodLOOK for radioisotope with SHORTEST half-life and

LEAST mass

PracticeWhich 10 g sample of these radioisotopes will decay to the greatest extent in 50 years?1)Kr-852) H-3 3) Cs-137 4) Sr-90

Which sample will have the greatest amount of its isotope remaining after 60 seconds?1)5 g of Ne-19 3) 5 g of Fr-2202)10 g of Ne-19 4) 10 g of Fr-220

The decaying process of a radioisotope can be represented with graphs, diagrams and data tables.

Time (days) Mass of radioisotope sample remaining (g)

0 160

4 120

8 80

12 60

16 40

20 30

24 20

28 15

32 10

Determining mass from the data and graphoriginal mass = mass at time zero = 160 g½ original mass = mass after 1 half-life period = 80 g 1/4th

original mass = mass after 2 half-life periods = 40 g1/8th original mass = mass after 3 half-life periods = 20 g

Determining time from the data and graphhalf-life = time when (80 g), ½ original mass remained = 8 daystwo half-life periods = time when (40 g), ¼ original mass remained = 16 daysThree half-life periods = time when (20 g), 1/8 of original mass = 24 days

Determining which radioisotope from the data and graphLOOK for a radioisotope on Table N with the half-life of about 8 days = I-131

Tracer – radioisotope that is used to follow the path of a chemical reaction

Radioisotope tracers in medical treatments and diagnoses must have a short half-life and be quickly eliminated from the body

Radioisotope tracers for dating usually have very long half-life

Radioisotope name

Radioisotope symbol

Common application

Field of application

Iodine-131 131I Thyroid disorder; diagnosis and treatment

medical

Technetium-99 99Tc Cancer tumor diagnosis

medical

Cobalt-60 60Co Cancer treatment

medical

Iron-56 56Fe Blood disorder treatment

medical

Carbon-14 14C Tracer for chemical reaction

research

Carbon-14 and Carbon-12

14C12C

Fossilized dating Archeological dating

Uranium-238 and Lead-206

238U206Pb

Rock dating Geological dating

Radioisotope waste•Wastes and radiations produced from nuclear reactors are highly dangerous to life on earth•Prolong and high dose exposure to radiation can cause serious health issues, and sometimes death•Radiation from nuclear power must be well contained to protect humans and other living things•Nuclear wastes are equally dangerous because they are highly radioactive•Nuclear wastes need to be stored in safe areas to protect the public from being exposed to themSolid wastes (highly radioactive) Gas wastes90Sr 222Rn137Cs 85Kr

16N