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Question

In YDSE, an electron beam is used to obtain interference pattern, If speed of electron is increased then

A
no interference pattern will be observed.
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B
distance between two consecutive fringes will increase.
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C
distance between two consecutive fringes will decrease.
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D
distance between two consecutive fringes remains same.
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Solution

The correct option is C distance between two consecutive fringes will decrease.
We have
λ=hmv

whereλ is the wavelength. h is Planck's constant, m is the mass and vv is the velocity.
λ1v

If the velocity of an electron increases then wavelength decreases.
Also we have fringe width,
β=λDd

βλ
Since wavelength decreases, fringe width will also decrease.

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