# During the nuclear explosion, one of the products is $^{90}Sr$  with a half-life of 6.93 years. If was absorbed in the bones of a newly born baby in place of Ca, how much time, in the year, is required to reduce it by 90% if it is not lost metabolically----------- Option: 1 23.03 Option: 2 46.06 Option: 369.06 Option: 422.66

We know this formula:-

$\\\mathrm{t\: =\: \frac{2.303}{k}log\frac{[R_{o}]}{[R]}}$

For 90% completion, the required time will be -

$\\\\\mathrm{t\: =\: \frac{2.303}{k}log\frac{[R_{o}]}{[0.1R_{o}]}}$

$\\\mathrm{t\: =\: \frac{2.303}{k}log10}$

$\\\mathrm{t\: =\: \frac{2.303}{k}}$

Half-life is given as 6.93 years. So,
$\\\mathrm{k\: =\: \frac{0.693}{t_{\frac{1}{2}}}}$

$\\\mathrm{k\: =\: \frac{0.693}{6.93}\: =\: 0.1}$

Thus, t is given as fro 90% completion:

$\\\mathrm{t\: =\: \frac{2.303}{k}}$

$\\\mathrm{t\: =\: \frac{2.303}{0.1}}$

Thus, t = 23.03 years

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