Question

A color television tube also generates some x rays when its electron beam strikes the screen. What is the shortest wavelength of these x rays, if a 30.0-kV potential is used to accelerate the electrons? (Note that TVs have shielding to prevent these x rays from exposing viewers.)

Short answer

As a result, the x-ray wavelength is 4.136 x 10^-11 m.

Step-by-step solution

Determine the formulas:

Consider the formula for the energy of X ray photons as follows:

\[E = \frac{{hc}}{\lambda }\]

Here,

λ= Wavelength

E = Energy of the x-ray photons

h = Planck's constant

c = Speed of light

Consider the formula for the energy in terms of the voltage as follows:

\[E = qV\]

Here,

q = Charge

V = Voltage applied

Calculating the shortest wavelength of x-rays

Rearrange the formula for the energy in terms of the wavelength as:

\[E = \frac{{hc}}{\lambda }\]

Substituting the values, wavelength is calculated as

\[\begin{array}{c}\lambda = \frac{{\left( {6.626 \times {{10}^{ - 34}}{\rm{J}} \cdot {\rm{s}}} \right)\left( {3 \times {{10}^*}\;\frac{{\rm{m}}}{{\rm{s}}}} \right)}}{{\left( {1.6012 \times {{10}^{ - 19}}{\rm{C}}} \right)\left( {30 \times {{10}^3}\;{\rm{V}}} \right)}}\\\lambda = 4.136 \times {10^{ - 11}}\;\;{\rm{m}}\end{array}\]

Hence, the wavelength of the x-ray is 4.136 x 10^-11 m.