Chapter 31, Problem 44P

To determine

To show:About $35\text{eV}$ required to produce one ion pair is consistent with two definition.

Explanation of Solution

Given data:

The two definitions of roentgen are:

1. Ion produced by the radiation is $1.6\times {10}^{12}$ ion pairs/g ,and

2. Deposited by the radiation $0.878\times {10}^{-2}\text{J}/\text{kg}$ .

Start with the current definition and relate them by the value of $35\text{eV}$ per ion pair.

  $\begin{array}{l}\text{R}=\left(0.878\times {10}^{-2}\frac{\text{J}}{\text{kg}}\right)\left(\frac{1\text{kg}}{1000\text{g}}\right)\left(\frac{1\text{eV}}{1.60\times {10}^{-19}\text{J}}\right)\left(\frac{1\text{ ion }\mathrm{pair}}{35\text{eV}}\right)\\ =1.567\times {10}^{12}\text{ ion pairs }/\text{g}\end{array}$

The two values of ion pairs per gram are within about $2\mathrm{\%}$ of each other.

Conclusion About $35\text{eV}$ required to produce one ion pair is consistent with two definition.