Question

After three 'average life times' of a radioactive sample, the amount of substance remains x% of the original amount. Then, approximate value of x is

• A. 14
• B. 37
• C. 7
• D. 5

Answer 1

The correct option is D 5

We know that decay constant $\lambda =1/T$, where $T$ is average lifetime

So using $N=N_0{e}^{-\lambda t}$ and putting $t=3T$

We get $N=N_0{e}^{-3}=N_0/e^3=N_0/(2.7{)}^3=0.0498N_0=N_0\times 4.8/100=4.98$ % $of$ $N_0$

Here we can see that present amount $N$ is $4.98$% of initial amount $N_0$ i.e. value of $x$ is approximately $5$

Option D is correct.