Question

The shortest wavelength of X-rays produced in an X-ray tube depends upon which of the following:
(A) Nature of gas in tube
(B) Atomic number of the target element
(C) Voltage applied to the tube
(D) Atmospheric conditions

Answer 1

When an electron is accelerated through a potential difference V and is targeted towards a target material, it loses some of its energy in the form of continuous X-Rays. This loss of energy is due to Coulomb interaction. When, electron loses all of its energy at a time then X-Rays of shortest wavelength are produced.So,we are going to use this concept in order to solve this problem.

Formula used:
${\lambda _{cut - off}} = \dfrac{{12400}}{V}\mathop A\limits^o$

Complete step by step answer:
X-rays were first discovered by Roentgen in 1895, when he X-rayed his wife’s hand. X-rays are produced when highly energetic electrons (accelerated through potential V) are directed towards a target heavy-atom (generally Tungsten). Due to the Coulomb interaction between the electron and the nucleus of the atom, electrons lose their energy in the form of
continuous X-Rays. When the electrons hit the orbital electrons of the heavy atom, characteristic X-rays are produced. The electron which has taken the place of the orbital electron is in an excited state. When it returns back to ground state, it produces the said X-Rays.So, for the shortest wavelength, the electron has to lose all of its energy as wavelength is inversely proportional to the energy. More the energy, less the wavelength. The electron has to lose all its energy which it gained through its acceleration in the potential V. Therefore,

$$\lambda = \dfrac{{hc}}{E} = \dfrac{{hc}}{{2meV}} \\\ \lambda = \dfrac{{12400}}{V}\mathop A\limits^o \\\$$

Where,H is the Planck constant,m is the mass of the electron and e is the electronic charge.
So, we note from the relation that the shortest wavelength depends upon the voltage applied in the Coolidge tube.
The correct answer is option C.

Note: Do not get confused between characteristic and continuous X-rays. The characteristic X-Rays always have a higher wavelength in comparison to the continuous wavelength. The shortest wavelength will occur when an electron loses all its energy and this will happen only in Continuous X-Rays.