Question

The activity of a radioactive sample falls from 600 s^(-1) to 500 s^(-1) in 40 minutes. Calculate its half-life.

Answer 1

Hence the half life of the radioactive sample is t^(1/2) = 152 minutes

Explanation:

A = A0 e^(-M)

500 s^(-1) = (600 s^(-1) e^(-M)

e^(-M) = 5/6

λt = ln (5/6)

Or

λ = ln (5/6)  / t = ln (6/5) / 40 min

The half life is t^(1/2) = ln 2 / λ

t^(1/2) = ln (2) / ln (6/5) x 40 min

t^(1/2) = 152 minutes

Hence the half life of the radioactive sample is t^(1/2) = 152 minutes