Chapter 28, Problem 31P

To determine

The voltage across the tube.

Answer to Problem 31P

  $\text{41}\text{kV}$

Explanation of Solution

Given info:

Wavelength, $\text{λ}\text{=}0.030nm$

Formula used:

  $\text{λ=}\frac{\left(\text{1}\text{.24}{\text{×10}}^{\text{3}}\text{eV}\cdot \text{nm}\right)}{\text{E}}$

Where, $\text{λ}$ is a wavelength and $\text{E}$ is energy in eV .

Calculation:

The shortest wavelength X-ray has the most energy. This energy is the maximum kinetic energy of the electron in the tube:

  $\begin{array}{c}\text{E}\text{=}\frac{\left(\text{1}\text{.24}{\text{×10}}^{\text{3}}\text{eV}\cdot \text{nm}\right)}{\text{λ}}\\ =\frac{\left(\text{1}\text{.24}{\text{×10}}^{\text{3}}\text{eV}\cdot \text{nm}\right)}{\left(\text{0}\text{.030}\text{nm}\right)}\\ =\text{4}\text{.1}\times {\text{10}}^4\text{eV}\\ \text{=}\text{41}\text{keV}\end{array}$

Hence, the operating voltage of the tube is $\text{41}\text{kV}$

Conclusion:

The required value is $\text{41}\text{kV}$ .