Question

The number of disintegration per minute of a certain radioactive substance are 6050 initially and 4465 at the end of one hour. Calculate the decay constant and the half life of the substance.

Answer 1

We know that R = R₀ e^-λt

6080 = R₀ e^λt

4465 = R₀ e^-λ(t+60)

^{\(\frac {6080}{4465} = \frac {e^{-λt}}{e^{-λt}} e^{-60λ}\)}

e^+60λ =^{\(\frac {6080}{4465} \)}

e^+60λ= 1.354

60λ = ln (1.354)

λ = \(\frac {1}{60}\) ln (1.354)

λ = \(\frac {0.30}{60}\)

Decay constant λ = 0.005 m

Half life

T_1/2 = \(\frac {0.693}{λ}\)

 T_1/2 = \(\frac {0.693}{0.005}\)

 T_1/2 = 138.6 min