Physics - Modern Physics Question with Solution | TestHub

Given half-life $T_{1/2}=5$ years and time $t=10$ years.

Number of half-lives $n=\frac{t}{T_{1/2}}=\frac{10}{5}=2$

Fraction of sample remaining after $n$ half-lives is given by $\frac{N}{N_0}={\left(\frac{1}{2}\right)}^n$

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

Fraction of sample decayed $=1-\frac{N}{N_0}=1-\frac{1}{4}=\frac{3}{4}$

Percentage of fraction decayed $=\frac{3}{4}\times 100\%=75\%$

Answer: $75\%$