Question

During nuclear explosion one of the products is $^{90}Sr$ with half-life of $28.1 \,yr$. If $1 \mu g$ of $^{90}Sr$ was absorbed in the bones of a newly born body instead of calcium, how much of it will remain after $60 \,yr$, if it is not lost metabolically?

• A. $0.184\, \mu g$
• B. $0.025\, \mu g$
• C. $0.262\, \mu g$
• D. $0.228\, \mu g$

Answer 1

Answer: (D)

Half-life

$t _{1 / 2} =28.1 \,yr $

$k =\frac{0.693}{t_{1 / 2}}=\frac{0.693}{28.1}\, yr ^{-1}$

For first order reaction,

$t =\frac{2.303}{k} \log \frac{a}{(a-x)} $

$a =1 \,\mu, t=60 \,yr , k=\frac{0.693}{28.1} \,yr ^{-1} $

$60 \,yr =\frac{2.303}{0.693 / 28.1} \times \log \frac{ a }{( a - x )} $

$\log \frac{ a }{( a - x )} =\frac{\left.(60 yr ) \times 0.693 / 28.1 yr ^{-1}\right)}{2.303}=0.642 $

$\frac{ a }{( a - x )} $ =antilog $0.642=4.385$

$(a-x)=\frac{a}{4.385}=\frac{(1 \mu g)}{4.385}=0.2280 \,\mu\, g$

Amount left after $60\, yr =0.2280 \,\mu \,g$