Question

One gram of a radioactive sample of half-life $10\text{min}$ is sealed in a capsule at time $t=0$. Amount of sample decayed upto $5\text{min}$ is:

• A. $0.293\text{g}$
• B. $0.5\text{g}$
• C. $0.25\text{g}$
• D. $0.707\text{g}$

Answer 1

The correct option is A $0.293\text{g}$

We know, $N=N_0{e}^{-\lambda t}$
where the decay constant $\lambda =\left(0.693/T_{half}\right)$.

Given, $T_{half}=10\text{min}$

Therefore, after $t=5\text{min}$
$N=N_0{e}^{(-0.693/10)\times 5}$
$=1\times e^{-0.693/2}=0.707\text{g}$
So, the amount of sample decayed is $(1–0.707)=0.293\text{g}$