Which equation allows you to calculate the wavelength of electromagnetic radiation if you know only its frequency?

• A. c = λν
• B. ν = λ / c
• C. λ = h / p
• D. E = hν

Answer: (A)

Verified step by step guidance

1. Recall the fundamental relationship between the speed of light (c), wavelength (\lambda), and frequency (\nu) of electromagnetic radiation, which is given by the equation: \(c = \lambda \nu\).
2. Understand that in this equation, \(c\) is the speed of light (approximately \$3.00 \times 10^{8}\( m/s), \)\lambda\( is the wavelength (in meters), and \)\nu$ is the frequency (in hertz).
3. To find the wavelength when the frequency is known, rearrange the equation to solve for \(\lambda\): \(\lambda = \frac{c}{\nu}\).
4. Note that the other given equations relate to different concepts: \(\nu = \frac{\lambda}{c}\) is incorrect dimensionally, \(\lambda = \frac{h}{p}\) relates wavelength to momentum (de Broglie wavelength), and \(E = h\nu\) relates energy to frequency.
5. Therefore, the correct equation to calculate wavelength from frequency is \(c = \lambda \nu\), or equivalently, \(\lambda = \frac{c}{\nu}\).