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.