Answer :
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.
2*29 years - 1/2*1/2 *1 kg.
Answer: 58 years
Explanation:
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Radioactive decay follows first order kinetics.
Half-life of strontium-9 = 29 years
[tex]\lambda =\frac{0.693}{t_{\frac{1}{2}}}=\frac{0.693}{29}=0.024year^{-1}[/tex]
[tex]N=N_o\times e^{-\lambda t}[/tex]
N = amount left after time t = 0.25 kg
[tex]N_0[/tex] = initial amount = 1 kg
[tex]\lambda[/tex] = rate constant
= 0.024
t= time = ?
[tex]0.25kg=1kg\times e^{- 0.024 years^{-1}\times t years}[/tex]
[tex]t=58years[/tex]
Thus it takes 58 years to a 1 kg sample of strontium-90 decay and reduce to 0.25 kg of strontium-90.
