Question:

Given below are two statements : Two photons having equal linear momenta have equal wavelengths. If the wavelength of photon is decreased, then the momentum and energy of a photon will also decrease. In the light of the above statements, choose the correct answer from the options given below.

Updated On: Dec 30, 2025
  • Both Statement I and Statement II are true
  • Statement I is false but Statement II is true
  • Both Statement I and Statement II are false
  • Statement I is true but Statement II is false
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The Correct Option is D

Solution and Explanation

To solve this problem, let's analyze each statement individually and use our understanding of the physics of photons, specifically their momentum and energy properties.

  1. Statement I: "Two photons having equal linear momenta have equal wavelengths."
    - The momentum of a photon (\(p\)) is given by the equation \(p = \frac{h}{\lambda}\), where \(h\) is Planck's constant and \(\lambda\) is the wavelength of the photon.
    - If two photons have equal linear momentum, then:\(\frac{h}{\lambda_1} = \frac{h}{\lambda_2}\)- Simplifying this equation yields \(\lambda_1 = \lambda_2\), indicating the wavelengths are equal. Hence, Statement I is true.

 

  1. Statement II: "If the wavelength of a photon is decreased, then the momentum and energy of a photon will also decrease."
    - As established, the momentum of a photon is inversely proportional to its wavelength: \(p = \frac{h}{\lambda}\).
    - This means that if the wavelength (\(\lambda\)) decreases, the momentum (\(p\)) actually increases, contrary to the statement's claim that it decreases. - Energy (\(E\)) of a photon is given by \(E = \frac{hc}{\lambda}\) (where \(c\) is the speed of light).
    - As the wavelength decreases, the energy increases, again contrary to the statement which claims a decrease. Thus, Statement II is false.

Combining these analyses, we conclude that the correct answer is: Statement I is true but Statement II is false.

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Concepts Used:

Photoelectric Effect

When light shines on a metal, electrons can be ejected from the surface of the metal in a phenomenon known as the photoelectric effect. This process is also often referred to as photoemission, and the electrons that are ejected from the metal are called photoelectrons.

Photoelectric Effect Formula:

According to Einstein’s explanation of the photoelectric effect :

The energy of photon = energy needed to remove an electron + kinetic energy of the emitted electron

i.e. hν = W + E

Where,

  • h is Planck’s constant.
  • ν is the frequency of the incident photon.
  • W is a work function.
  • E is the maximum kinetic energy of ejected electrons: 1/2 mv².

Laws of Photoelectric Effect:

  1. The photoelectric current is in direct proportion to the intensity of light, for a light of any given frequency; (γ > γ Th).
  2. There exists a certain minimum (energy) frequency for a given material, called threshold frequency, below which the discharge of photoelectrons stops completely, irrespective of how high the intensity of incident light is.
  3. The maximum kinetic energy of the photoelectrons increases with the increase in the frequency (provided frequency γ > γ Th exceeds the threshold limit) of the incident light. The maximum kinetic energy is free from the intensity of light. 
  4. The process of photo-emission is an instantaneous process.