Question

What is the energy of a photon of frequency \( \nu \)?

• A. \(E = mc^2\)
• B. \(E = hv\)
• C. \(E = \frac{1}{2}mv^2\)
• D. \(E = \frac{h}{\nu}\)

Hint:

Photon energy can also be written in terms of wavelength using \(c = \lambda \nu\): \[ E = \frac{hc}{\lambda} \] This relation is widely used in problems involving photoelectric effect, spectroscopy, and atomic transitions.

Answer 1

The Correct Option is B

Concept: According to Planck's quantum theory, energy is emitted or absorbed in discrete packets called quanta. In the case of electromagnetic radiation, each quantum of light is called a photon. The energy of a photon depends directly on the frequency of the radiation and is given by Planck's relation.

Step 1: State Planck's energy equation. The energy of a photon is given by: \[ E = h\nu \] where:
• \(E\) = energy of the photon
• \(h\) = Planck's constant \((6.626 \times 10^{-34} \, J\,s)\)
• \(\nu\) = frequency of the radiation

Step 2: Interpretation of the equation. From the equation we observe:
• Energy is directly proportional to frequency.
• Higher frequency radiation (like X-rays or gamma rays) has higher photon energy.
• Lower frequency radiation (like radio waves) has lower photon energy.

Step 3: Final expression. Thus, the energy of a photon with frequency \( \nu \) is \[ \boxed{E = h\nu} \]