Back to Directory
NEET PHYSICSMedium

A parallel beam of fast-moving electrons is incident normally on a narrow slit. A fluorescent screen is placed at a large distance from the slit. If the speed of the electrons is increased, which of the following statements is correct?

A

The angular width of the central maximum of the diffraction pattern will increase.

B

The angular width of the central maximum will decrease.

C

The angular width of the central maximum will be unaffected.

D

A diffraction pattern is not observed on the screen in the case of electrons.

Step-by-Step Solution

According to de Broglie's hypothesis, the wavelength of an electron is inversely proportional to its momentum (and hence speed), given by λ=hmv\lambda = \frac{h}{mv}. When the speed (vv) of the electrons is increased, their de Broglie wavelength (λ\lambda) decreases. The angular width of the central maximum in a single slit diffraction pattern is directly proportional to the wavelength, given by 2θ=2λa2\theta = \frac{2\lambda}{a}, where aa is the slit width. Therefore, a decrease in wavelength results in a decrease in the angular width of the central maximum.

Practice Mode Available

Master this Topic on Sushrut

Join thousands of students and practice with AI-generated mock tests.

Get Started