Question

The half-life of ${}^{131}I$ is $8$ days. Given a sample of ${}^{131}I$ at time $t=0$

• A. No nucleus will decay before $t=4$ days
• B. No nucleus will decay before $t=8$ days
• C. No nuclei will decay before $t=16$ days
• D. A given nucleus may decay at any time after $t=0$

Answer 1

The correct option is D A given nucleus may decay at any time after $t=0$

As nucleus decay is a continuous process, it takes several half life to decay completely.

$T^{\frac{1}{2}}=8$days

After 4 days

$N=N_0{\left(\frac{1}{2}\right)}^{\frac{4}{8}}=\frac{N_0}{\sqrt{2}}$

Affter 8 days

$N=N_0{\left(\frac{1}{2}\right)}^{\frac{8}{8}}=\frac{N_0}{2}$

After 16 days

$N=N_0{\left(\frac{1}{2}\right)}^{\frac{16}{8}}=\frac{N_0}{4}$

These equations prove all the options wrong, except for when t=0 because when t=0

$N=N_0{\left(\frac{1}{2}\right)}^{\frac{0}{8}}=N_0$

Hence, A given nucleus may decay any time after t=0