Q.

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

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By Expert Faculty of Sri Chaitanya

The angular width of the central maximum will decrease.

The angular width of the central maximum will be unaffected.

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

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

answer is 1.

(Detailed Solution Below)

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Detailed Solution

de Broglie wavelength of an electronλ=hp=hmvwhere 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 θ0=2λawhere a is the width of slit.If λ decreases, θ0 will decreaseTherefore, the correct statement is (a).

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