Question

The half-life of a radioactive element is $2n$ yr. The fraction decayed in $n$ year is:

• A. 1.414
• B. 0.29
• C. 0.414
• D. 0.1

Answer 1

Answer: (B)

0.29

As we know,

$t=\frac{2.303}{\lambda }\log \frac{r_0}{r}$

$N=N_0{e}^{-\lambda t}=N_0{e}^{-(ln2\times n)/2n}=N_0/\sqrt{2}$

$\therefore Fractiondecayed=\frac{(N_0-N)}{N_0}=\frac{\sqrt{2}-1}{\sqrt{2}}=0.29$