A radioactive element has a rate of disintegration 10,000 disintegrations per minute at a particular instant. After four minutes it becomes 2500 disintegrations per minute. The decay constant per minute is

Question

A radioactive element has a rate of disintegration 10,000 disintegrations per minute at a particular instant. After four minutes it becomes 2500 disintegrations per minute. The decay constant per minute is, 0.2 log e 2 ⁡, 0.5 log e 2 ⁡, 0.6 log e 2 ⁡, 0.8 log e 2 ⁡

MARKS App · Accepted Answer

N N 0 = e - λ t ∴ 2500 10000 = e - λ × 4 ∴ 1 4 = e - 4 λ ∴ e 4 λ = 4 ∴ 4 λ = log e ⁡ 4 ∴ 4 λ = log e ⁡ 2 2 ∴ 4 λ = 2 log e ⁡ 2 ∴ λ = 2 4 log e ⁡ 2 ∴ λ = 0.5 log e ⁡ 2

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