Question

What is the half-life period of a radioactive material if its activity drops to 1/16 th of its initial value in 30 years?

• A. 9.5 years
• B. 8.5 years
• C. 7.5 years
• D. 10.5 years

Answer 1

Answer: (C)

7.5 years

Answer 2

The correct answer is (C) : 7.5 years
$∵A=\frac{A0}{\frac{t}{2^{T_{1/2}}}}$
$⇒2^{\frac{t}{T_{1/2}}}$
$=\frac{A_0}{A}=16$
$⇒\frac{t}{T_{1/2}}=4$
$⇒\frac{30}{T_{1/2}}=4$
$⇒T_{1/2}=\frac{30}{4}$
=7.5 years