Statement I : Two photons having equal linear momenta have equal wavelengths. Statement II : If the wavelength of photon is decreased, momentum and energy will also decrease.
Show Hint
- Both true
- Both false
- I true, II false
- I false, II true
The Correct Option is C
Solution and Explanation
To analyze the given statements, let's start by understanding the properties of photons and how their momentum and energy are related to their wavelength.
Concepts:
- Photon Momentum and Wavelength: 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.
- Photon Energy: The energy E of a photon is given by E = \frac{hc}{\lambda}, where c is the speed of light.
Analysis of Statement I:
If two photons have equal linear momenta, according to the formula p = \frac{h}{\lambda}, they must have equal wavelengths. Therefore, Statement I is true.
Analysis of Statement II:
If the wavelength \lambda of a photon is decreased, according to p = \frac{h}{\lambda}, the momentum p will increase since p is inversely proportional to \lambda. Also, from E = \frac{hc}{\lambda}, the energy E will increase as well because energy is also inversely proportional to wavelength. Therefore, Statement II is false.
Conclusion: The correct interpretation is that Statement I is true, and Statement II is false. Thus, the correct answer is: I true, II false.
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