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  4. A radioactive sample at some instant has a disintegration rate of 5000 disintegrations per minute. After 5 minutes, the rate becomes 1250 disintegrations per minute. Then, the decay constant (per minute) is

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Q. A radioactive sample at some instant has a disintegration rate of $5000$ disintegrations per minute. After $5$ minutes, the rate becomes $1250$ disintegrations per minute. Then, the decay constant (per minute) is

NTA AbhyasNTA Abhyas 2022

Solution:

$\frac{ A }{ A _{0}}=\frac{1250}{5000}=\frac{1}{4}=\left(\frac{1}{2}\right)^{\frac{ t }{ T }}$
$\Rightarrow \text{T} = \frac{\text{t}}{2} = \frac{\text{5}}{2}$
$\lambda =\frac{\text{ln} 2}{\text{T}}=\frac{2}{5}l\text{n}2$
$=\text{0.4}ln2$