Which of the following best describes the relationship between the frequency (ν) and wavelength (λ) of electromagnetic radiation?

• A. They are directly proportional; as frequency increases, wavelength also increases.
• B. They are inversely proportional; as frequency increases, wavelength decreases.
• C. They are both constant for all types of electromagnetic radiation.
• D. They are unrelated; frequency and wavelength change independently.

Answer: (B)

Verified step by step guidance

1. Recall the fundamental relationship between the speed of light (c), frequency (\nu), and wavelength (\lambda) of electromagnetic radiation, which is given by the equation: \[ c = \nu \times \lambda \]
2. Understand that the speed of light (c) is a constant in a vacuum, approximately \(3.00 \times 10^{8} \text{ m/s} \), meaning it does not change for different types of electromagnetic waves.
3. Since \( c \) is constant, if the frequency (\nu) increases, the wavelength (\lambda) must decrease to keep the product \( \nu \times \lambda \) equal to \( c \). This shows an inverse relationship between frequency and wavelength.
4. Express the inverse proportionality explicitly by rearranging the equation: \[ \lambda = \frac{c}{\nu} \] This formula shows that wavelength is inversely proportional to frequency.
5. Conclude that as frequency increases, wavelength decreases, and vice versa, which means frequency and wavelength are inversely proportional.