Explanation:

When a beam of accelerated electrons hit a target, a continuous X-ray spectrum is emitted from the target. This is because the electrons in the beam collide with the atoms in the target, causing the electrons in the atoms to move to higher energy levels. When these electrons return to their original energy levels, they release energy in the form of X-rays.

The energy of the X-rays emitted depends on the energy levels of the electrons in the atoms that are involved in the transition. The energy levels of the electrons in an atom are quantized, which means they can only have certain discrete values of energy. This means that the X-ray spectrum emitted from the target will be a series of discrete lines, with each line corresponding to a different energy transition in the atoms.

However, in addition to these discrete lines, there will also be a continuous background of X-rays emitted. This background is due to the fact that the electrons in the beam have a range of energies, and so they can cause a range of energy transitions in the atoms. This results in a continuous spectrum of X-rays being emitted.

Now, coming to the question, it asks which one of these wavelengths is absent in the X-ray spectrum if the X-ray tube is operated at 40,000V. The answer is option 'A' which is 0.25 Å.

The reason for this is related to the energy of the X-rays emitted. The energy of an X-ray is related to its wavelength by the equation:

E = hc/λ

where E is the energy of the X-ray, h is Planck's constant, c is the speed of light, and λ is the wavelength of the X-ray.

When the X-ray tube is operated at 40,000V, the electrons in the beam have an energy of 40,000 electron volts (eV). This means that they can cause energy transitions in the atoms that result in X-rays with energies up to 40,000 eV. Using the equation above, we can calculate the corresponding shortest wavelength of X-rays emitted:

E = hc/λ

λ = hc/E

λ = (6.626 x 10^-34 J s x 3.0 x 10^8 m/s)/(40,000 eV x 1.602 x 10^-19 J/eV)

λ = 0.310 Å

This means that the X-ray spectrum emitted from the target will include X-rays with wavelengths down to 0.310 Å. However, any X-rays with shorter wavelengths than this will not be emitted, as the electrons in the beam do not have enough energy to cause the necessary energy transitions in the atoms. Therefore, the wavelength of 0.25 Å is absent in the X-ray spectrum.