Physics - Modern Physics Question with Solution | TestHub

The probability that a nucleus will not decay is-

$\left(\frac{N}{N_0}\right)={\left(\frac{1}{2}\right)}^{\mathrm{n}}=\mathrm{q}$

When n is the number of half-lives

$\mathrm{q}={\left(\frac{1}{2}\right)}^4=\frac{1}{16}$

The probability that a nucleus will decay is

$\mathrm{p}=1-\mathrm{q}=1-\frac{1}{16}=\frac{15}{16}$