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Half-Life

Key Concepts

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 t_½
Different radioisotopes have different half-lives.
The amount of radioactive isotope remaining can be calculated:
N_t = N_o x (0.5)^{number of half-lives}
Where:
N_t = amount of radioisotope remaining
N_o = original amount of radioisotope
number of half-lives = time ÷ half-life

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.

Number of Half-lives Time (years) % Strontium-90 remaining % Strontium-90 that has decayed

0 0 100 0

1 28 50 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 98.4375

Calculate the percentage of strontium-90 remaining after 280 years.
N_t = N_o x (0.5)^{number of half-lives}
N_t = ? %
N_o = 100%
number of half-lives = time ÷ half-life = 280 ÷ 28 =10
N_t = 100 x (0.5)¹⁰ = 0.098%