Question

Strontium-90 has a half-life of 29 years. In how many years will a 1 kg sample of strontium-90 decay and reduce to 0.25 kg of strontium-90?

Answer

58 years

116 years

87 years

29 years

Answer 1

Answer: 58 years

Explanation: -

Radioactive decay follows first order kinetics.

Half-life of strontium-9 = 29 years

`\lambda =\frac{0.693}{t_{(1)/(2)}}=(0.693)/(29)=0.024year^(-1)`

`N=N_o* e^(-\lambda t)`

N = amount left after time t = 0.25 kg

`N_0` = initial amount = 1 kg

`\lambda` = rate constant = 0.024

t= time = ?

`0.25kg=1kg* e^{- 0.024 years^(-1)* t years}`

`t=58years`

Thus it takes 58 years to a 1 kg sample of strontium-90 decay and reduce to 0.25 kg of strontium-90.

Answer 2

In 58 (2.29 yrs - 1/2.1/2 .1 kg ) years will a 1 kg sample of strontium-90 decay and reduce to 0.25 kg of strontium-90.
2*29 years - 1/2*1/2 *1 kg.