For the radioactive material half life is 10 minutes. If initially there are 800 number of nuclei the time taken (in minutes) for the disintegration of 600 nuclei is
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 20 minutes
In each half-life the number of undecayed nuclei falls to half. After \( n \) half-lives
\( \displaystyle N = \frac{N_0}{2^{n}} \)
600 of the 800 nuclei disintegrate, so the number left is
\( N = 800 - 600 = 200 \)
\( \displaystyle \frac{N}{N_0} = \frac{200}{800} = \frac{1}{4} = \left(\frac{1}{2}\right)^{2} \;\Rightarrow\; n = 2 \)
\( t = n\,T_{1/2} = 2 \times 10 = 20\,\mathrm{minutes} \)