According to quantum theory applicable to electromagnetic radiation, the energy of a single photon (energy quantum) is proportional to which quantity?

Introduction / Context:
Photon energy connects wave and particle descriptions of electromagnetic radiation. In remote sensing, detector response and atmospheric processes depend on photon energy as well as radiance, making the proportionality between energy and frequency foundational.

Given Data / Assumptions:

• Planck’s relation applies to photons: E = h * f.
• h is Planck’s constant; f is frequency; λ is wavelength; c = f * λ.
• We consider single-photon energy, not macroscopic radiant energy.

Concept / Approach:
Planck’s relation states that photon energy is directly proportional to frequency and inversely proportional to wavelength (E = h * f = h * c / λ). Higher frequency (e.g., UV) means higher photon energy; lower frequency (e.g., microwave) means lower photon energy. This governs interactions like electronic transitions and thermal emission.

Step-by-Step Solution:
Recall E = h * f.Identify that “proportional to frequency” matches the formula.Select the option: “The frequency.”

Verification / Alternative check:
Spectral bands with shorter wavelengths (higher frequencies) carry higher energy photons, explaining stronger photochemical effects in UV compared to IR.

Why Other Options Are Wrong:

• Square, square root, or reciprocal relationships do not reflect Planck’s law.
• Energy is inversely—not directly—proportional to wavelength.

Common Pitfalls:
Confusing photon energy with power (energy per unit time); mixing up wavelength and frequency relationships.

Final Answer:
The frequency