1. Half-Life

2. Half-Life
The half-life of a radioisotope is the time required for half the atoms in a given sample to undergo radioactive, or nuclear, decay.
Half-life is given the symbol t½
Different radioisotopes have different half-lives.
The amount of radioactive isotope remaining can be calculated:     Nt = No x (0.5)number of half-lives
    Where:     Nt = amount of radioisotope remaining     No = original amount of radioisotope     number of half-lives = time ÷ half-life

3. Examples
Consider strontium-90 which has a half-life of approximately 28 years.
Initially, at time t=0, the sample is 100% strontium-90
After 28 years, only half the original amount of strontium will remain:     ½ x 100% = 50%
After another 28 years, only half of this amount of strontium-90 will remain:     ½ x 50% = 25%
After another 28 years, only half of this amount of strontium will remain:     ½ x 25% = 12.5%
and so on.
At any given time, the amount of strontium-90 that has undergone decay can be calculated:     amount of strontium-90 decayed = the original amount - the amount remaining.

4. % Strontium-90 remaining
Number of Half-lives
Time (years)
% Strontium-90 remaining
% Strontium-90 that has decayed
100 1 28 50 2 56 25 75 3 84
12.5
87.5 4
112
6.25
93.75 5
140
3.125
96.875 6
168
1.5625

6. Calculate the percentage of strontium-90 remaining after 280 years.
1)What are we looking for? Remaining sample
2)What do we know?
Nt = ? % No = 100%
number of half-lives = 10
(time ÷ half-life = 280 ÷ 28 =10)
3) What is the formula?
Formula: Nt = No x (0.5)number of half-lives
4) Solve.
Nt = 100 x (0.5)10 = 0.098%

7. Practice solving problems:
Ex: The radioisotope Tc-99m is used in bone scans. Tc-99 has a half-life of 6 hours. If a dose of 100 mg is given to the patient, how much sample remains in the body of a patient that had a Tc-99m bone scan after 24 hours?

8. Bell Work:
Ex: The half-life of radium-226 is 1,600 years. How many milligrams of radium-226 remain after 8,000 years if the original sample is mg?
The half-life of iodine-131 is 8 days. How many milligrams of iodine-131 remain after 48 days if the original sample was 100 mg?
Radon-222 has a half-life of 4 days. After 16 days, you have 6.25 mg of given sample of radon left. How much radon was in the original sample?