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

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.

Answer 2

Answer: 58 years

Explanation: -

Radioactive decay follows first order kinetics.

Half-life of strontium-9 = 29 years

$\lambda =\frac{0.693}{t_{\frac{1}{2}}}=\frac{0.693}{29}=0.024year^{-1}$

$N=N_o\times e^{-\lambda t}$

N = amount left after time t  = 0.25 kg

$N_0$ = initial amount  = 1 kg

$\lambda$ = rate constant = 0.024

t= time  = ?

$0.25kg=1kg\times e^{- 0.024 years^{-1}\times t years}$

$t=58years$

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