Chapter 32, Problem 32.12QAP

Interpretation Introduction

Interpretation:

The relative standard of counting rate $\frac{{\sigma }_R}{R}=M^{-1/2}$ is to be proved.

Concept introduction:

The counting rate is calculated by the following formula-

$R=\frac{M}{t}$ …………… (1)

And standard deviation for counting rate is given as-

${\sigma }_R=\frac{{\sigma }_M}{t}$ …………… (2)

Standard deviation is-

${\sigma }_M=\sqrt{M}$ …………… (3)

Relative standard deviation is for counting rate = $\frac{{\sigma }_R}{R}$ …………… (4)

Where,

M = counts

t = time

${\sigma }_M$ = standard deviation for M

${\sigma }_R$ = relative standard deviation