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

Question

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

MARKS App · Accepted Answer

As rate of disintegration is proportional to the number of atoms actually present, therefore, N 0 = 5000, N = 1 2 5 0 , t = 5 min As N = N 0 e - λ t ∴ ln N ⁡ N ⁡ 0 = - λ t ; ln 1 2 5 0 5 0 0 0 = - λ t ; ln 1 4 = - λ × 5 ; - 2 ln 2 = - λ × 5 ; λ = 0 . 4 ln 2

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