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

The Correct Option is 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 \times10 $

$ = 20 $ minute