Question

10% of a radioactive sample has decayed 2 days, decayed percentage be:

• A. 19%
• B. 30%
• C. 81%
• D. 100%

Answer 1

The correct option is A 19%

10% of radioactive sample is decayed means,$N_0$

Let N is the number of nuclei left, $N=90$

So,

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

$\frac{N}{N_0}=e^{-2\lambda }$

$\frac{90}{100}=e^{-2\lambda }$

$\frac{9}{10}=e^{-2\lambda }$

$-\ln \left(\frac{9}{10}\right)=2\lambda ...........\left(1\right)$

Left nuclei is

$N=N_0{e}^{-2\lambda }$

$N=N_0{e}^{\ln \left(\frac{9}{10}\right)\times 2}$

$N=N_0\frac{81}{100}$

So, $81$% is left.

Decayed nuclei is $19$%