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Q.

Count rate of a radioactive substance is 400 per minute. After some time the count rate is 123 per minute. If half life of the element is 2 hours, then number of nuclei decayed in this interval is

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a

20, 875

b

47, 965

c

64, 625

d

32, 120

answer is D.

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Detailed Solution

$R_{1} = {λN}_{1} and R_{2} = {λN}_{2}$

$\begin{array}{l} ∴ {λN}_{1} - {λN}_{2} = R_{1} - R_{2} \\ \Rightarrow \frac{\ln 2}{T} (N_{1} - N_{2}) = R_{1} - R_{2} \\ \Rightarrow N_{1} - N_{2} = \frac{T (R_{1} - R_{2})}{\ln 2} = \frac{2 \times 60 \times (400 - 123)}{0 .693} \\ \Rightarrow N_{1} - N_{2} = 47, 965 \end{array}$

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