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Assertion : The energy (E ) and momentum...

Assertion : The energy `(E )` and momentum `(p)` of a photon are related by `p = E//c`.
Reason : The photon behaves like a particle.

A

If both assertion and reason are true and reason is the correct explanation of assertion

B

If both assertion and reason are true but reason is not the correct explanation of assertion

C

If assertion is true but reason is false

D

If both assertion and reason are false

Text Solution

AI Generated Solution

The correct Answer is:
To solve the question, we need to analyze the assertion and reason provided: ### Step 1: Understanding the Assertion The assertion states that the energy \( E \) and momentum \( p \) of a photon are related by the equation: \[ p = \frac{E}{c} \] where \( c \) is the speed of light. This relationship is derived from the principles of quantum mechanics and special relativity. ### Step 2: Deriving the Relationship 1. **Energy of a Photon**: The energy of a photon can be expressed as: \[ E = h \nu \] where \( h \) is Planck's constant and \( \nu \) is the frequency of the photon. 2. **Momentum of a Photon**: The momentum \( p \) of a photon can also be expressed using its wavelength \( \lambda \): \[ p = \frac{h}{\lambda} \] 3. **Relating Wavelength and Frequency**: The wavelength \( \lambda \) and frequency \( \nu \) are related by the equation: \[ c = \lambda \nu \implies \lambda = \frac{c}{\nu} \] 4. **Substituting Wavelength into Momentum Equation**: \[ p = \frac{h}{\lambda} = \frac{h \nu}{c} \] Since \( E = h \nu \), we can substitute \( E \) into the momentum equation: \[ p = \frac{E}{c} \] ### Step 3: Understanding the Reason The reason states that "the photon behaves like a particle." This is consistent with the concept of wave-particle duality in quantum mechanics, where photons exhibit both wave-like and particle-like properties. ### Step 4: Conclusion Both the assertion and the reason are correct: - The assertion \( p = \frac{E}{c} \) is a valid relationship for photons. - The reason correctly explains that photons behave like particles, which justifies the assertion. ### Final Answer Both the assertion and the reason are correct, and the reason is a correct explanation of the assertion.

To solve the question, we need to analyze the assertion and reason provided: ### Step 1: Understanding the Assertion The assertion states that the energy \( E \) and momentum \( p \) of a photon are related by the equation: \[ p = \frac{E}{c} \] where \( c \) is the speed of light. This relationship is derived from the principles of quantum mechanics and special relativity. ...
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