Question

In YDSE, an electron beam is used to obtain interference patterns. If speed of the electron is increased
(a) Number interference pattern will be observed.
(b) Distance between the consecutive fringes will be increased.
(c) Distance between the two consecutive fringes will be decreased.
(d) Distance between the two consecutive fringes remains the same.

Answer 1

In this question,we can use the concept of De-Broglie wavelength and fringe width relation obtained by Young Double Slit experiment.

Complete Step by Step Answer:
We have equation according to de-Broglie
$\lambda = \dfrac{h}{{mv}}$ ……………(i)
Where $\lambda$the wavelength h is is planck's constant, m is the mass and v is velocity
$\Rightarrow \lambda \times \dfrac{1}{V}$
Wavelength is inversely proportional to velocity means if the velocity of an electron increases than wavelength decreases.
According to young's double slit experiment equation for fringe width is
$\beta = \dfrac{{\lambda D}}{d}$ ……………(ii)
Where $\beta$ is fringe width, $\lambda$ is wavelength. D is the distance between slits and screen, d is slit width.
$\Rightarrow \beta \times \lambda$
Hence
$\beta \times \lambda \times \dfrac{1}{V}$ ……………(iii)
Hence in above relation it is clear that fringe width is directly proportional to wavelength and inversely proportional to velocity. So if the speed of the electron is increased then distance between the two consecutive fringe's will be decreased.

The correct option is (C): distance between the two consecutive fringes will be decreased.

Note: : In young's double slit experiment the interference pattern is obtained in the focal plane of a micrometre eyepiece and with its help fringe width $\beta$ is measured. By measuring the distance d between the two covert sourced and their distance D from the eyepiece, the value of wavelength $\lambda$ can be calculated as
$\lambda = \dfrac{{\beta d}}{D}$