Question

Three-fourth of the active nuclei present in a radioactive sample decay in $\frac{3}{4}$ second. What ls the half-life of the sample?

• A. 1 second
• B. $\frac{1}{2}$ second
• C. $\frac{3}{4}$ second
• D. $\frac{3}{8}$ second

Answer 1

Answer: (D)

$\frac{3}{8}$ second

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

As $\lambda$ is constant:

$\frac{0.639}{t_{1/2}}=\lambda$ ......(1)
$\lambda =\frac{2.303}{t_{3/4}}\log \left(\frac{100}{75}\right)$.....(2)
Equating (1) and (2):
$2t_{1/2}=3t_{3/4}$
So, $t_{1/2}=\frac{3}{4}\times \frac{1}{2}=\frac{3}{8}$ seconds