Question

The wavelength of an electron.
(A) Is equal to that of light.
(B) Remains constant with velocity.
(C) Decreases with increasing velocity.
(D) Increases with decreasing velocity.

Answer 1

Wavelength of light: It is defined as the distance between the identical points in the adjacent cycle of a waveform along a wire. Planck’s constant: It is a constant having value equal to $6.26 \times {10^{ - 34}}$ . It is represented by $h$ .

Complete step by step solution
First of all let us talk about wavelength of light, speed of light and planck’s constant.
Speed of light: The speed by which light travels in the air, is known as speed of light, The value of speed of light in air is constant and has the value $3 \times {10^8}m/\sec$ .
Wavelength of light: It is defined as the distance between the identical points in the adjacent cycle of a waveform along a wire. The unit of wavelength is centimetre, metre and millimetres. It is represented by $\lambda$ .
Frequency: It is defined as the number of occurrences of a repeating event per unit of time. It is measured in the unit of hertz. It is represented by $\nu$ .
Wave number is defined as the number of waves in a unit distance. It is reciprocal of wavelength (which is length of single cycle in a wave). Wavelength can be measured as velocity of the wave divided by its frequency. Hence wave number can be measured as frequency of the wave divided by the velocity of the wave.
Wavelength of an electron is calculated as $\lambda = \dfrac{h}{{mv}}$ , where $h$ is the planck’s constant, $m$ is mass of an electron and $v$ is the velocity of the wave.
From here it is clear that wavelength of an electron is inversely proportional to the velocity of the wave. Hence wavelength increases with decrease in the wavelength and wavelength decreases with increase in the wavelength.
So option C and D are correct.

Note
Planck’s constant: It is a constant having value equal to $6.26 \times {10^{ - 34}}$ . It is represented by $h$ .
Mass of an electron is very small and numerically it is approximately equal to the value of $9.1 \times {10^{ - 31}}Kg$ .