Question

In a Coolidge tube
A) The intensity of x-rays is controlled by filament current
B) The intensity of x-rays is controlled by the accelerating voltage.
C) As the accelerating voltage is increased ${\lambda _{\min }}$​ is decreased
D) ${\lambda _{\min }}$ is controlled by filament current
A. a, c.
B. b, d.
C. b, c.
D. a, d.

Answer 1

To solve this question, we should remember some basic concepts of the Coolidge tube and X-rays. Coolidge tube has a high vacuum and its use of a heated filament as the source of electrons. There is so little gas inside the tube that it is not involved in the production of x-rays, unlike the situation with cold cathode gas discharge tubes.

Complete step-by-step answer :
The discovery of X-rays was accidentally made by a German professor Rontgen in 1895. In the laboratory, X-rays can be produced by using the Coolidge ray tube. Their frequency range is ${10^{16}}$ to $3 \times {10^{19}}$ Hz.
The advantage of the Coolidge tube is its stability and the fact that the intensity and energy of the X-rays can be controlled independently. Increasing the current to the cathode increases its temperature. This increases the number of electrons emitted by the cathode, and as a result, the intensity of the X-rays. Increasing the high voltage potential difference between the anode and the cathode increases the velocity of the electrons striking the anode, and this increases the energy of the emitted X-rays.
In the Coolidge tube, the electrons are produced by thermionic effect from a tungsten filament heated by an electric current. The filament is the cathode of the tube.
The high voltage potential is between the cathode and the anode, the electrons are thus accelerated, and then hit the anode. So, the intensity of X-rays is controlled by filament current. And in this process the incoming electrons transfer their energy to the X-rays that are then emitted from the sample. The maximum energy (or the minimum wavelength) X-rays are produced when all the energy is transferred. This is the short wavelength limit (SWL) of the continuous X-rays. The wavelength is related to the applied voltage by the following relation:
$eV = \dfrac{{hc}}{\lambda }$
Thus, as the applied voltage increases the SWL decreases.
Hence, the correct answer is option (A) – (a,c).

Note : As the cathode filament is heated, it emits electrons. The hotter the filament gets, the greater the emission of electrons. These electrons are accelerated towards the positively charged anode and when the electrons strike the anode, they change direction and emit bremsstrahlung, i.e. x-rays with a continuous range of energies. The maximum energy of the x-rays is the same as the kinetic energy of the electrons striking the anode.