First slide

Diffraction

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 statements is correct?

Moderate

A

The angular width of the central maximum will decrease.
B

The angular width of the central maximum will be unaffected.
C

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

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

Solution

de Broglie wavelength of an electron
$λ = \frac{h}{p} = \frac{h}{m v}$
where m is the mass and v is the speed of the electron respectively.
If speed v of electron is increased, momentum p (= mv) will increase. Hence, wavelength $λ$ will decrease.
Angular width of the central maximum is $θ_{0} = \frac{2 λ}{a}$ where a is the width of slit.
If $λ$ decreases, $θ_{0}$ will decrease
Therefore, the correct statement is (a).

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