Question

Two radioactive substances $X$ and $Y$ initially contain an equal number of atoms. Their half-lives are $1$ hour and $2$ hours respectively. Then the ratio of their rates of disintegration after two hours is.

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

Answer 1

The correct option is A $1:1$

Their disintegration constant will be in ratio of $\frac{{\lambda }_1}{{\lambda }_2}=\frac{t_2}{t_1}=\frac{2}{1}=2$, $t_1$ $t_2$ are their half lives.

If their initial number of atoms are $N_0$ then after $2$ hour

so for first sample is will be $2$ half lives so remaining atoms $N_1=\frac{N_0}{2^2}$

And for second sample is will be just $1$ half life so remaining atoms $N_2=\frac{N_0}{2^1}$

so their activity ratio after 2 houe will be $\frac{A_1}{A_2}=\frac{N_1{\lambda }_1}{N_2{\lambda }_2}=\frac{1\times 2}{2\times 1}=\frac{1}{1}$