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

Let's analyze each statement provided regarding photons, and determine their validity based on established physics principles.

1. Analysis of Statement I: "Two photons having equal linear momenta have equal wavelengths."
   • The momentum (\( p \)) of a photon is given by the formula: p = \frac{h}{\lambda}, where \( h \) is Planck's constant and \( \lambda \) is the wavelength.
   • For two photons to have equal momenta, \frac{h}{\lambda_1} = \frac{h}{\lambda_2}. Given \( h \) is a constant, this implies \lambda_1 = \lambda_2.
   • Thus, Statement I is true.
2. Analysis of Statement II: "If the wavelength of a photon is decreased, then the momentum and energy of a photon will also decrease."
   • Photon energy (\( E \)) is given by \( E = \frac{hc}{\lambda} \), where \( c \) is the speed of light.
   • If the wavelength \( \lambda \) decreases, then \frac{1}{\lambda} increases, indicating the energy \( E \) increases.
   • For momentum, since \( p = \frac{h}{\lambda} \), as \( \lambda \) decreases, \( p \) increases.
   • Therefore, Statement II is false.
3. Conclusion: Considering the above analysis, Statement I is true but Statement II is false. Hence, the correct option is: "Statement I is true but Statement II is false."