Which of the following statements correctly describes the relationship between the wavelength and frequency of electromagnetic radiation?

• A. As the frequency increases, the wavelength remains constant.
• B. As the wavelength increases, the frequency increases.
• C. As the wavelength increases, the frequency decreases.
• D. Wavelength and frequency are independent of each other.

Answer: (C)

Verified step by step guidance

1. Recall the fundamental relationship between the wavelength (\( \lambda \)) and frequency (\( \nu \)) of electromagnetic radiation, which is given by the equation: \[ c = \lambda \times \nu \] where \( c \) is the speed of light in a vacuum (approximately \( 3.00 \times 10^{8} \, \text{m/s} \)).
2. Understand that since the speed of light \( c \) is a constant, the product of wavelength and frequency must always equal this constant value.
3. From the equation, if the wavelength \( \lambda \) increases, then the frequency \( \nu \) must decrease to keep the product \( \lambda \times \nu \) equal to \( c \). Conversely, if the frequency increases, the wavelength must decrease.
4. Analyze each statement in the problem: - "As the frequency increases, the wavelength remains constant" is incorrect because \( \lambda \) must change if \( \nu \) changes. - "As the wavelength increases, the frequency increases" is incorrect because they are inversely related. - "Wavelength and frequency are independent of each other" is incorrect because they are directly linked by the speed of light.
5. Conclude that the correct description is: "As the wavelength increases, the frequency decreases," reflecting the inverse relationship between wavelength and frequency in electromagnetic radiation.