A proton and alpha particle is accelerated through the same potential which one of the two has

CBSE Class 12
1

a proton and alpha particle is accelerated through the same potential which one of the two has

  1. greater value of de-Broglie wavelength associated with it?
  2. less kinetic energy?
2

A proton and an a-particle are accelerated through the same potential. Which one of the two has
(i) greater value of de-Broglie wavelength associated with it and
(ii) less kinetic energy?
Give reasons to justify your answer.
Solution:

  1. Using de-Broglie wavelength formula, we already know that proton and alpha particle are accelerated through the same potential.
    So, both their velocities are same.
    image
    Therefore, proton has a greater de-Broglie wavelength than the alpha particle.

  2. For same potential of acceleration, K.E is directly proportional to the ‘q’
    As, the charge of an alpha particle is more than the proton,
    hence proton has a lesser value of Kinetic Energy (K.E)