## Conceptual Physics (12th Edition)

From our study of wave motion, page 362, we know that $f = \frac{c}{\lambda}$, where c is the speed of light. The photon frequency is inversely proportional to its wavelength. Doubling the wavelength means halving the frequency. For photons, E = hf, where E is the energy, h is Planck's constant, and f is the photon's vibrational frequency. Half the frequency means half the energy per photon. This is discussed on page 564. In summary, twice the wavelength means half the frequency, which means one-half the energy per photon.