Question

The half life of a radioactive material is $5years$. The probability of disintegration for a nucleus in $10years$ is

• A. $0.50$
• B. $0.25$
• C. $0.60$
• D. $0.75$

Answer 1

The correct option is D $0.75$

Ten years means $\frac{10}{5}=2Half-lives$ so just put $n=2$ in $N=N_0(\frac{1}{2}{)}^n$ we get $remaining$ nuclei, $N=N_0/4$

i.e. ${\frac{1}{4}}^{th}$ of initial nuclei

so probability of decay will be $\frac{N_0-N}{N_0}=0.75$

Option D is correct.