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Q.

The half-life of a radioactive material is four hours. If the initial amount is 400g then after 24 hours it will remain

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a

46.80g

b

93.75g

c

9.37g

d

6.25g

answer is D.

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Detailed Solution

$N u m b e r o f h a l f l i v e s = n = \frac{t}{T_{\frac{1}{2}}} = \frac{24}{4} = 6 h r' s D e c a y L a w i n t e r m s o f m a s s, \frac{m}{m_{0}} = {(\frac{1}{2})}^{n}; m_{0} = 400 g \Rightarrow m = m_{0} {(\frac{1}{2})}^{6} = \frac{400}{2^{6}} = \frac{400}{64} = 6.25 g$

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The half-life of a radioactive material is four hours. If the initial amount is 400g then after 24 hours it will remain