29. 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 ?

29. 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) Diffraction pattern is not observed on the screen in case of electrons

Answer :  (b) The angular width of the central maximum will decrease

\(\lambda = \frac{h}{p}\)

\(= \frac{h}{mv}\)

\(\text{As } v \uparrow, \ \lambda \downarrow\)

\(\theta_w = \frac{\lambda}{a}\)

\(\text{As } \lambda \downarrow, \ \theta_w \downarrow\)