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 Max Planck's Quantum Theory, light is not continuous but consists of small packets of energy called quanta (or photons).
Step 1: Understanding the Question:
We need the basic equation that relates the energy of a single photon to its frequency.
Step 2: Key Formula or Approach:
The energy of a photon is directly proportional to its frequency.
\[ E \propto \nu \]
To convert this to an equation, we use Planck's constant (\(h\)).
Step 3: Detailed Solution:
The fundamental relationship is:
\[ E = h\nu \]
Where:
- \(E\) = Energy of the photon.
- \(h\) = Planck's constant \(\approx 6.626 \times 10^{-34} \, J \cdot s\).
- \(\nu\) (nu) = Frequency of the electromagnetic radiation.
Step 4: Final Answer:
The energy of a photon is given by \(E = h\nu\).