Question

Two radioactive sources $A$ and $B$ initially contain equal number of radioactive. Source $A$ has a half-life of $1hour$ and source $B$ has a half-life of $2hours$. the ratio of the rate of disintegration of $A$ to that of $B$ is:

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

Answer 1

The correct option is B $2:1$

We know, $t_{1/2}=\frac{lo{g}_{e}2}{K}$

Given, Half life of A $\left(t_A\right)=1hr$ $=\frac{lo{g}_{e}2}{K_A}$

And, Half life of A $\left(t_B\right)=2hr$ $=\frac{lo{g}_{e}2}{K_B}$

$\Rightarrow \frac{t_A}{t_B}=\frac{K_B}{K_A}$

$\Rightarrow \frac{K_A}{K_B}=\frac{2}{1}$

Therefore, B is correct option.