Question

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 statement is correct?

• A. Diffraction pattern is not observed on the screen in the case of electrons
• B. The angular width of the central maximum of the diffraction pattern will increase
• C. The angular width of the central maximum will decreases
• D. The angular width of the central maximum will remain unaffected

Answer 1

Answer: (C)

The angular width of the central maximum will decreases

We know that $\lambda =\frac{h}{mv}$

Also for angular width

$\omega =\frac{2\lambda }{d}$

So we can say $\omega \propto \lambda \propto \frac{1}{v}$

So if the velocity increases, the angular width of the central maximum will decrease.