N atoms of a radioactive element emit n alpha particles per... | PHYSICS - RADIOACTIVITY | SolveeIt | Solveeit

Today, August 19

Question

N atoms of a radioactive element emit n alpha particles per second. The half life of the element is.

A

$\frac{n}{N}$ sec

B

$\frac{N}{n}$ sec

C

$\frac{0.693\mspace{6mu} N}{n}$ sec

D

$5,099\mspace{6mu} cm^{- 1}$ sec

Answer

$\frac{0.693\mspace{6mu} N}{n}$ sec

Explanation

Solution

$\frac{dN}{dt} = - \lambda N \Rightarrow n = - \lambda N$ (Given $\frac{dN}{dt} = n$ )

$\therefore\lambda = - \frac{n}{N}\mspace{6mu}\mspace{6mu}\therefore$ Half life

$= \frac{0.693}{\lambda} = \frac{0.693}{\lambda} = \frac{0.693\mspace{6mu} N}{n}\sec$