Question

${}^{\prime }{N}^{\prime }$ atoms of a radioactive element emit ${}^{\prime }{n}^{\prime }$ alpha particles per second at an instant. Then the half-life of the element is :

• A. $\frac{n}{N}sec.$
• B. $1.44\frac{n}{N}sec.$
• C. $0.69\frac{n}{N}sec.$
• D. $0.69\frac{N}{n}sec.$

Answer 1

The correct option is D $0.69\frac{N}{n}sec.$

$n=\lambda N$
$\lambda =\frac{n}{N}$
$\therefore t_{1/2}=\frac{0.69}{\lambda }=\frac{0.69N}{n}$