Question

Ten percent of a radioactive sample has decayed in $1\text{day}$. After $2\text{days}$, the decayed percentage of nuclei will be

• A. $81\%$
• B. $19\%$
• C. $20\%$
• D. $50\%$

Answer 1

The correct option is B $19\%$

From the law of radioactive decay,

The $N^{\prime }$ number of nuclei decayed as a function of time is given by,

$N^{\prime }=N_0(1-e^{-\lambda t})$

For case 1:

$N_1=N_0-N_0{e}^{-\lambda t}$

Given that $N_1=\frac{N_0}{10},t=1\text{day}$

$\Rightarrow e^{-\lambda \left(1\right)}=\frac{9}{10}$

For case 2:

$t=2\text{days}$

$\Rightarrow N_2=N_0-N_0{e}^{-\lambda \left(2\right)}$

$\Rightarrow N_2=N_0-N_0{\left(e^{-\lambda }\right)}^{\left(2\right)}$

$\Rightarrow N_2=N_0-\frac{81}{100}{N}_0$

$\Rightarrow N_2=\frac{19}{100}{N}_o$

$\Rightarrow N_2=19\%of{N}_0$

Hence, option $\left(\text{B}\right)$ is correct.