The disintegration rate of a certain radioactive sample at any instant is 4750 disintegrations per minute. 5 minutes after, the rate becomes 2700 disintegrations per minute. Calculate the decay constant.(log₁₀ 1.76 = 0.2455).

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Solution

Disintegration rate is proportional to the number of atoms present.

∴

\frac{N_{0}}{N} = \frac{4750}{2700} = 1.76

Now, using the relation,

N = N_{0} e^{- λt}

\frac{N_{0}}{N} = e^{λt}

\Rightarrow

\log_{e} \frac{N_{0}}{N} = λt

\Rightarrow

λ = \frac{\log_{e} (N_{0} / N)}{t} = \frac{2.3026 \log_{10} (1.76)}{t}

\Rightarrow

λ

= \frac{2.3026 \times 0.2455}{5} = 0.1131 \min^{- 1} .

is the required value of decay constant.

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