Question

Two radioactive sources $X$ and $Y$ of half lives $1h$ and $2h$ respectively initially contain the same number of radioactive atoms. At the end of $2h$, their rates of disintegration are in the ratio of :

• A. $4:3$
• B. $3:4$
• C. $1:2$
• D. $2:1$

Answer 1

The correct option is C $1:2$

Rate of disintegration $\alpha$ number of atoms left

For $X\frac{N}{N_0}={\left(\frac{1}{2}\right)}^2=\frac{1}{4}$

For $Y\frac{N}{N_0}={\left(\frac{1}{2}\right)}^1=\frac{1}{2}$

$\therefore \frac{R_X}{R_Y}=\frac{\frac{N_0}{4}}{\frac{N_0}{2}}=\frac{1}{2}$