Modern Physics 4 Question 4

4. A particle A of mass ’ m ’ and charge ’ q ’ is accelerated by a potential difference of

50V. Another particle B of mass ’ 4m ’ and charge ’ q ’ is accelerated by a potential difference of 2500V. The ratio of de-Broglie wavelengths λAλB is close to

(a) 4.47

(b) 10.00

(c) 0.07

(d) 14.14

(Main 2019, 12 Jan I)

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Solution:

  1. de-Broglie wavelength associated with a moving charged particle of charge q is

λ=hp=h2mqV

where, V= accelerating potential.

Ratio of de-Broglie wavelength for particle A and B is,

λAλB=mBqBVBmAqAVA=mBmAqBqAVBVA

Substituting the given values, we get.

=4mmqq250050=2×1×5×1.414=14.14



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