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.

• A. Both Statement I and Statement II are true
• B. Statement I is false but Statement II is true
• C. Both Statement I and Statement II are false
• D. Statement I is true but Statement II is false

Answer 1

The Correct Option is D

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.