Question

The half life period of a radioactive element is $150$ days. After $600$ days $1\,g$ of the element will be reduced to

• A. $\frac{1}{32}\,g$
• B. $\frac{15}{16}\,g$
• C. $\frac{1}{8}\,g$
• D. $\frac{1}{16}\,g$

Hint:

First calculate the number of half-lives and then repeatedly divide the mass by 2.

Answer 1

The Correct Option is D

Concept: Half-life is the time required for a radioactive substance to reduce to half of its original mass. The remaining mass after \(n\) half-lives is \[ N=N_0\left(\frac12\right)^n \] where \[ n=\frac{t}{T_{1/2}} \]

Step 1: Calculate the number of half-lives. \[ T_{1/2}=150\text{ days} \] \[ t=600\text{ days} \] \[ n=\frac{600}{150}=4 \]

Step 2: Apply radioactive decay formula. Initial mass \[ N_0=1\,g \] Therefore, \[ N=1\left(\frac12\right)^4 \] \[ N=\frac1{16}\,g \]

Step 3: State the answer. After \(600\) days only \[ \frac1{16}\,g \] of the element remains. center minipage0.35

Remaining mass = $\frac1{16}\,g$ minipage center