Question

The masses of two radioactive substances are same and their half lives are $1$ year and $2$ years respectively. The ratio of their activities after 6 years will be

• A. 1:04
• B. 1:02
• C. 1:03
• D. 1:06

Answer 1

Answer: (A)

1:04

Answer 2

Let initial activity of both substances are same.
$\therefore R=R_{0}\left(\frac{1}{2}\right)^{n}=R_{0}\left(\frac{1}{2}\right)^{t / t_{1 / 2}}$
$\Rightarrow \frac{R_{1}}{R_{2}}=\frac{\left(\frac{1}{2}\right)^{4 / 1}}{\left(\frac{1}{2}\right)^{4 / 2}}=\frac{\left(\frac{1}{2}\right)^{4}}{\left(\frac{1}{2}\right)^{2}}=\left(\frac{1}{2}\right)^{2}$
$\Rightarrow \frac{R_{1}}{R_{2}}=\frac{1}{4}$