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One of the hazards of nuclear explosion is the generation of Sr⁹⁰ and its subsequent incorporation in bones. This nuclide has a half-life of 28.1 years. Suppose one microgram was absorbed by a new-born child, how much Sr⁹⁰ will retain in his bones after 20 years?

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0.7321 $μ g$

0.6107 $μ g$

0.5814 $μ g$

0.2142 $μ g$

answer is B.

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Detailed Solution

For the half lite t_½ = 28.1 yr the decay constant is

$K = \frac{0 .693}{t_{1 / 2}} = \frac{0 .693}{28 .1}$

Since the radioactivity decay follows the first order kinetics,

$\begin{array}{l} ∴ \log \frac{[A]}{[A_{0}]} = - \frac{K}{2 .303} t \\ \log \frac{[A]}{1 .0 μg} = - \frac{0 .693}{28 .1} \times \frac{20}{2 .303} \end{array}$

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