A freshly prepared sample of a radioisotope of half-life 1386 s has activity ${10}^{3}$ disintegrations per…

A freshly prepared sample of a radioisotope of half-life 1386 s has activity ${10}^{3}$ disintegrations per second. Given that In 2 = 0.693, the fraction of the initial number of nuclei (expressed in nearest integer percentage) that will decay in the first 80 s after preparation of the sample is

Solution

f = 1 - e - λ t = 1 - e - λ t ≈ 1 - 1 - λ t = λ t
f = 0.04
Hence  % decay  ≈  4 % :

Asked in: JEE Advanced 2013 (Paper 1)

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