Question

Given that the accelerating voltage in the Coolidge tube is V, what is the range of wavelengths you will find in the x-ray spectrum (in appropriate units)?

• A.
  
  
• B.
  
• C.
  
• D.

Answer 1

The correct option is B


The wavelength of such a photon would eventually depend on its energy. The minimum wavelength will correspond to the maximum energy and the maximum wavelength will correspond to the minimum energy. So let's think about what can be the minimum and maximum energies of a photon?
If the accelerating voltage is V, the energy supplied to the electron is eV. The X-Ray photons are emitted when an electron loses its energy. The energy of an x-ray photon would depend on what amount of energy has it got, out of the total energy of the electron.
If we think about the extreme cases, the maximum energy a photon may have is equal to the total energy of the electron eV (when an electron looses all its energy at once in form of a photon) and the minimum energy a photon may have tends to zero (when an electron looses all its energy in form of heat).

So, for minimum wavelength;
${\lambda }_{min}=\frac{hc}{E_{max}}=\frac{hc}{eV}$
And for maximum wavelength;
${\lambda }_{max}=\frac{hc}{E_{min}}=\frac{hc}{0}=\infty$
So, the range is
$\frac{hc}{eV}\to \infty$.