A radioactive sample at any instant has its disintegration rate 5000 disintegrations per minute . After 5 minutes , the rate is 1250 disintegrations p - Physics MCQ AIEEE 2003 2026 | ExamTest.live

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A radioactive sample at any instant has its disintegration rate 5000 disintegrations per minute . After 5 minutes, the rate is 1250 disintegrations per minute . Then, the decay constant (per minute) is:

Solution & Step-by-step Explanation

The rate of disintegration R = R_{0} e^{- λ t} . 1250 = 5000 e^{- 5 λ} \frac{1}{4} = e^{- 5 λ} 4 = e^{5 λ} ⟹ ln 4 = 5 λ 2 ln 2 = 5 λ ⟹ λ = \frac{2}{5} ln 2 = 0.4 ln 2 .

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A radioactive sample at any instant has its disintegration rate 5000 disintegrations per minute . After 5 minutes, the rate is 1250 disintegrations per minute . Then, the decay constant (per minute) is:

0.4 ln 2

0.2 ln 2

0.1 ln 2

0.8 ln 2

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