Chapter 24, Problem 83A

Interpretation Introduction

Interpretation:

The distnace of gamma emission intensity drop to $\text{0}\text{.15mrem}/{\text{sm}}^{\text{2}}$ needs to be determined.

Concept introduction:

The intensity of radiation depends on the distance from the source.

Answer to Problem 83A

Distance at which the gamma emission intensity drops to $\text{0}\text{.15mrem}/{\text{sm}}^{\text{2}}$ is 2.2m.

Explanation of Solution

Given information,

$\begin{array}{c}{\text{γ}}_{{\text{I}}_{\text{1}}}=\text{0}{\text{.75mrem/sm}}^{\text{2}}\\ {\text{d}}_{\text{1}}=\text{1m}\\ {\text{γ}}_{{\text{I}}_{\text{2}}}=\text{0}{\text{.15mrem/ms}}^{\text{2}}\end{array}$

Relation between intensity and distance is

$\begin{array}{c}{\text{I}}_{\text{1}}{\text{d}}_{\text{1}}{}^{\text{2}}={\text{I}}_{\text{2}}{\text{d}}_{\text{2}}{}^{\text{2}},\text{I}\text{is}\text{the}\text{intensity}\\ \text{d}\text{is}\text{the}\text{distance}\\ {\text{d}}_{\text{2}}{}^2=\frac{{\text{I}}_{\text{1}}{\text{d}}_{\text{1}}{}^{\text{2}}}{{\text{I}}_{\text{2}}}\\ {\text{d}}_{\text{2}}{}^{\text{2}}=\frac{0.75{(1)}^2}{\text{0}\text{.15}}\\ {\text{d}}_{\text{2}}{}^{\text{2}}=5\\ {\text{d}}_{\text{2}}=\sqrt{5}\\ {\text{d}}_{\text{2}}=2.2\text{m}\end{array}$

Conclusion

The best way to get less intensity of radiation is just move away from the source.