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In a Young double slit experiment, the distance between the slits is 50 μm and the distance of the screen from the slits is 5 cm. An infrared monochromatic light is mood to produce an interference pattern with fringe width 1 mm. If the light source is replaced by an electron source to produce the same fringe width then the speed of the electrons is approximately
  1. 700m/s
  2. 7000m/s
  3. 70m/s
  4. 70000m/s

A
70m/s
B
700m/s
C
7000m/s
D
70000m/s
Solution
Verified by Toppr

We know that :- w=λDd
Given :- d=50×106m, w=5×102m and w=103m

λ=wdD=103×50×1065×102m

λ=106m

For an electron to produce same fringe width, its de-Broglie wavelength should be same as λ.

Now,for electron:-
λ=hmv

v=hmλ

v=6.63×10349.1×1031×106m/s

v700m/s

Hence, answer is option-(B).

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