Question:

The energy of a photon is equal to the kinetic energy of a proton. The energy of the photon is E. Let λ1 \lambda_1 be the de-Broglie wavelength of the proton and λ2 \lambda_2 be the wavelength of the photon. The ratio λ1λ2 \frac{\lambda_1}{\lambda_2} is proportional to

Updated On: Jul 29, 2022
  • E0 E^0
  • E12 E^{\frac{1}{2}}
  • E1 E^{-1}
  • E2 E^{-2}
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The Correct Option is B

Solution and Explanation

λ1λ2=h2mEhcE  or  λ1λ2?E1/2 \frac{\lambda_1}{\lambda_2} = \frac{\frac{h}{\sqrt2mE}}{\frac{hc}{E}} \, \, or\, \, \frac{\lambda_1}{\lambda_2} ? E^{1/2} Therefore, the correct option is (b)
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Concepts Used:

Kinetic energy

Kinetic energy of an object is the measure of the work it does as a result of its motion. Kinetic energy is the type of energy that an object or particle has as a result of its movement. When an object is subjected to a net force, it accelerates and gains kinetic energy as a result. Kinetic energy is a property of a moving object or particle defined by both its mass and its velocity. Any combination of motions is possible, including translation (moving along a route from one spot to another), rotation around an axis, vibration, and any combination of motions.