If photon A has twice the wavelength of photon B, how does the frequency of photon A compare to that of photon B?

• A. Photon A has the same frequency as photon B.
• B. Photon A has twice the frequency of photon B.
• C. Photon A has four times the frequency of photon B.
• D. Photon A has half the frequency of photon B.

Answer: (D)

Verified step by step guidance

1. Recall the fundamental relationship between the speed of light (\(c\)), wavelength (\(\lambda\)), and frequency (\(\nu\)) of a photon: \[c = \lambda \times \nu\]
2. Since the speed of light \(c\) is constant for all photons, we can express frequency in terms of wavelength as: \[\nu = \frac{c}{\lambda}\]
3. Given that photon A has twice the wavelength of photon B, we can write: \[\lambda_A = 2 \times \lambda_B\]
4. Substitute \(\lambda_A\) into the frequency equation for photon A: \[\nu_A = \frac{c}{\lambda_A} = \frac{c}{2 \times \lambda_B} = \frac{1}{2} \times \frac{c}{\lambda_B}\]
5. Recognize that \(\frac{c}{\lambda_B}\) is the frequency of photon B (\(\nu_B\)), so: \[\nu_A = \frac{1}{2} \times \nu_B\] This means photon A has half the frequency of photon B.