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. 20
• B. 30
• C. 10
• D. 15

Answer 1

The Correct Option is A

Method 1: Using Radioactive Decay Law

Given:

• Half-life \( T = 10 \) minutes
• Initial nuclei \( N_0 = 600 \)
• Disintegrated nuclei = 450
• Remaining nuclei \( N = 150 \)

Formula:

\[ N = N_0 \left(\frac{1}{2}\right)^{t/T} \]

Substituting values:

\[ 150 = 600 \left(\frac{1}{2}\right)^{t/10} \]

Simplifying:

\[ \frac{150}{600} = \frac{1}{4} = \left(\frac{1}{2}\right)^{t/10} \]

\[ \left(\frac{1}{2}\right)^2 = \left(\frac{1}{2}\right)^{t/10} \]

Comparing powers:

\[ \frac{t}{10} = 2 \Rightarrow t = 20 \text{ minutes} \]