Q: A certain substance decays to 1/32 of its initial activity in 25 days. Calculate its half- life.

Sol: Since , $\large N = N_0 (\frac{1}{2})^n $ ;Where n = number of half life .

$\large \frac{N_0}{32} = N_0 (\frac{1}{2})^n $

n = 5

$\large 5 = \frac{25}{T_{1/2}}$

T_{1/2} = 5 days