Question

In an x-ray tube, x-rays are produced by electrons accelerated by V volt.The maximum frequency of x-rays produced is
${\text{A}}{\text{. eVh}} \\\ {\text{B}}{\text{. }}\dfrac{{hV}}{e} \\\ {\text{C}}{\text{. }}\dfrac{{eh}}{V} \\\ {\text{D}}{\text{. }}\dfrac{{eV}}{h} \\\$

Answer 1

Hint: X-rays are electromagnetic waves which satisfy the energy relation for electromagnetic radiation. The acceleration produced in electrons in the tube is due to the charge on them and the voltage applied to the tube.

Complete step-by-step answer:
The electromagnetic radiation travels with the speed of light and comprises quantas of energy called photons. Einstein gave the relation for energy of electromagnetic radiation using the Planck’s constant. Through photoelectric effect, it was noticed that energy of the electromagnetic radiation depends on the frequency of the radiation.
$E = h\nu$
Where h is called the Planck’s constant and value $6.626 \times {10^{ - 34}}Js$.
X-rays are also electromagnetic radiations and produced when electrons by accelerating electrons. The energy supplied to the electron is equal to the product of electronic charge and voltage applied. If we equate this energy with the above relation we can get the maximum value of frequency of the x-rays generated. Therefore we can write that
$h\nu = eV \\\ \Rightarrow \nu = \dfrac{{eV}}{h} \\\$
which is the maximum frequency of x-rays. Therefore the correct answer is option D.

Additional information:
Planck’s law laid the foundation of quantum mechanics followed by Einstein’s photoelectric effect results. All energy comes in forms of packets called quanta of energy. Photon is the quanta of light which has rest mass equal to zero.

Note: This relation of energy $E = h\nu$ can be related to wavelength through the following relation $c = \nu \lambda$. It does not depend on the intensity of the incident radiation as proved by the results of the photoelectric effect for which Einstein got a Nobel prize.