Which of the following best describes the relationship between the energy of electromagnetic radiation and its wavelength?

• A. Energy is directly proportional to wavelength.
• B. Energy is proportional to the square of the wavelength.
• C. Energy and wavelength are unrelated.
• D. Energy is inversely proportional to wavelength.

Answer: (D)

Verified step by step guidance

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