Ncert Exercises & Solutions

Which sample A or B shown in figure has shorter mean-life?

Hint: The decay rate is equal to the slope of the graph.

Step 1: Find the initial decay rate.

From the given figure, we can say that;

at t = 0, {(\frac{dN}{dt})}_{A} = {(\frac{dN}{dt})}_{B}

\Rightarrow λ_{A} {(N_{0})}_{A} = λ_{B} {(N_{0})}_{B}

Step 2: Find the final decay rate.

Considering any instant t by drawing a line perpendicular to the time axis, we find that;

{(\frac{dN}{dt})}_{A} > {(\frac{dN}{dt})}_{B} \Rightarrow λ_{A} N_{A} > λ_{B} N_{B}

∴ N_{A} > N_{B} (rate of decay of B is slower)

∴ λ_{B} > λ_{A}

\Rightarrow τ_{A} > τ_{B} [∵ Average life τ = \frac{1}{λ}]