Question

For a radioactive material, half-life is $10$ minutes. If initially there are $600$ number of nuclei, the time taken (in minutes) for. the disintegration of $450$ nuclei is

• A. 15
• B. 20
• C. 30
• D. 10

Answer 1

Answer: (B)

Number of nuclei remaining $=600-450=150$
$\frac{N}{N_0}={\left(\frac{1}{2}\right)}^n$
$\frac{150}{600}={\left(\frac{1}{2}\right)}^{\frac{t}{t_{\frac{1}{2}}}}$
${\left(\frac{1}{2}\right)}^2={\left(\frac{1}{2}\right)}^{\frac{t}{t_{1/2}}}$
$t=2t_{1/2}=2\times 10$
$=20$ minute