Which of the following relation is true:
Photon Energy Momentum Relation Explained
This question relates a photon's energy (E) and momentum (P) to its angular frequency (ω) and wave number (k).
Key Physics Principles
The energy and momentum of a photon are defined by the following fundamental relations:
- Energy: E = &planckbarω
- Momentum: P = &planckbark
Here, &planckbar represents the reduced Planck constant (&planckbar = h / (2π)).
Deriving the Relationship
To find the relationship between E, P, ω, and k, we can express &planckbar in terms of E and P:
- From the energy equation: &planckbar = E / ω
- From the momentum equation: &planckbar = P / k
By setting these two expressions for &planckbar equal to each other:
$ \frac{E}{\omega} = \frac{P}{k} $
To match the format of the options, we rearrange this equation to express E:
$ E = \frac{\omega}{k} P $
Final Answer Verification
The derived equation E = (ω/k)P directly corresponds to Option D.
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