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

• A. Energy and wavelength both decrease together.
• B. Energy is independent of wavelength.
• C. Energy increases as wavelength decreases.
• D. Energy increases as wavelength increases.

Answer: (C)

Verified step by step guidance

1. Recall the fundamental relationship between the energy (E) of electromagnetic radiation and its wavelength (\lambda). The energy of a photon is given by the equation: \[E = \frac{hc}{\lambda}\] where \(h\) is Planck's constant and \(c\) is the speed of light.
2. Understand that in the equation, \(h\) and \(c\) are constants, so the energy \(E\) is inversely proportional to the wavelength \(\lambda\). This means as the wavelength increases, the energy decreases, and vice versa.
3. Analyze the options given in the problem by comparing them to the inverse relationship: - "Energy and wavelength both decrease together" implies a direct relationship, which is incorrect. - "Energy is independent of wavelength" contradicts the formula. - "Energy increases as wavelength decreases" matches the inverse proportionality. - "Energy increases as wavelength increases" is the opposite of the correct relationship.
4. Conclude that the correct description of the relationship is that energy increases as wavelength decreases, based on the inverse proportionality shown in the formula.
5. Remember that this relationship is fundamental in understanding electromagnetic radiation, such as why ultraviolet light has more energy than visible light, which in turn has more energy than infrared radiation.