Energy to Wavelength Calculator

The relationship between a photon's energy and its wavelength is governed by two fundamental constants of nature: Planck's constant (h) and the speed of light in a vacuum (c). The core formula linking energy (E in electron-volts) to wavelength (λ in meters) combines the Planck-Einstein relation and the wave propagation equation. First, the frequency (f) is determined by dividing the speed of light by the wavelength: f = c / λ. Next, the energy in joules is calculated using E = h * f, and then converted into electron-volts by dividing by the elementary charge.

Let us calculate the energy of a photon with a given wavelength of 500 nanometers (nm), which is 5 x 10^-7 meters. Using the speed of light c = 299,792,458 m/s, we first find the frequency: f = (299,792,458) / (5 x 10^-7) = 5.9958 x 10^14 Hz. Next, we apply Planck's constant (approximately 6.626 x 10^-34 joule-seconds) to find the energy in joules: (6.626 x 10^-34) * (5.9958 x 10^14) = 3.972 x 10^-19 joules. Finally, dividing by 1.60217 x 10^-19 to convert to electron-volts yields approximately 2.48 eV.

Always verify your unit prefixes before running calculations; converting nanometers, micrometers, or angstroms into meters is the most common source of error. Keep in mind that this calculator assumes propagation through a vacuum where the speed of light is at its maximum; if you are calculating for a medium like water or glass, the phase velocity of light must be adjusted accordingly.