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Question

If an electron and a proton have the same kinetic energy, the ratio of the de Broglie wavelengths of proton and electron would approximately be :
  1. 1 : 1837
  2. 43 : 1
  3. 1837 : 1
  4. 1 : 43

A
43 : 1
B
1 : 1837
C
1 : 43
D
1837 : 1
Solution
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E=12mv2

p=mv=2mE =2mqv

De Broglie wavelength associated with change particle

λ=hp=h2mE=h2mqν

where E=12mv2=K.E, P is momentum of change

So, λP=h2mpE

λe=h2meE

So, λpλe=memp

=memp

=9.1×10311.67×1027

=5.449×104

=2.33×102

=0.0233

=143

So, the answer is option (D).

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