Which of the following best describes the relationship between the energy of a photon and its wavelength?

• A. The energy of a photon is equal to the square of its wavelength.
• B. The energy of a photon is inversely proportional to its wavelength.
• C. The energy of a photon is independent of its wavelength.
• D. The energy of a photon is directly proportional to its wavelength.

Answer: (B)

Verified step by step guidance

1. Recall the fundamental relationship between the energy of a photon and its frequency, given by the equation \(E = h \nu\), where \(E\) is energy, \(h\) is Planck's constant, and \(\nu\) is the frequency of the photon.
2. Understand that the frequency \(\nu\) and wavelength \(\lambda\) of light are related by the speed of light \(c\) through the equation \(\nu = \frac{c}{\lambda}\).
3. Substitute the expression for frequency into the energy equation to get \(E = h \frac{c}{\lambda}\), showing that energy depends on wavelength.
4. Analyze the resulting formula to see that energy \(E\) is inversely proportional to wavelength \(\lambda\), meaning as wavelength increases, energy decreases, and vice versa.
5. Conclude that the correct description is that the energy of a photon is inversely proportional to its wavelength, not directly proportional or independent.