The rate of disintegration of a radioactive substance falls from 40 3 dps to 5 3 dps in 6 hours. The half-life of the radioactive substance is

Question

The rate of disintegration of a radioactive substance falls from 40 3 dps to 5 3 dps in 6 hours. The half-life of the radioactive substance is, 6 7 hours, 2 hours, 3 hours, 1 hour

MARKS App · Accepted Answer

A = A 0 e - λ t ⇒ 100 = 800 e - λ ( 6 × 60 ) ⇒ e - 350 x = 1 8 ⇒ - 360 λ = ln 1 8 = - ln 8 ⇒ λ = ln 2 3 360 = ln 2 120 ⇒ T 1 / 2 = ln 2 λ = ln 2 ( ln 2 / 120 ) = 120 minutes ⇒ T 1 / 2 = 2 hours

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