Question

After 2 hours, only 1/16th of the original decaying nuclei were present. What is th half-life of the sample?

Answer 1

If initially only $N_0$ amount of radioactive were present, then

after time $t=2hrs$, this reduce to $N=\frac{N_0}{16}$

using relation :-

$t=zlo{g}_2\frac{N_0}{N}$ (z= half-life period)

$\Rightarrow 2=2lo{g}_2\left(\frac{N_0}{N_0/16}\right)=zlo{g}_2\left(16\right)$

$\Rightarrow 2=42\Rightarrow z=\frac{2}{4}=\frac{1}{2}=30$ min