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

• A. As the wavelength increases, the energy decreases.
• B. Energy is always equal to the wavelength.
• C. Wavelength and energy are independent of each other.
• D. As the wavelength increases, the energy increases.

Answer: (A)

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 \(\nu\) (nu) is the frequency of the light wave.
2. Understand that the frequency \(\nu\) and wavelength \(\lambda\) of light are related by the speed of light \(c\) through the equation \(c = \lambda \nu\), where \(c\) is a constant (\$3.00 \times 10^8$ m/s).
3. Rearrange the equation to express frequency in terms of wavelength: \(\nu = \frac{c}{\lambda}\).
4. Substitute this expression for frequency into the energy equation to get \(E = h \frac{c}{\lambda}\), showing that energy is inversely proportional to wavelength.
5. Conclude that as the wavelength \(\lambda\) increases, the energy \(E\) decreases, which matches the correct answer choice.