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How to Convert Kiloelectron Volts Energy to Meters Wavelength

The standard units of measurement for energy are joules or calories, where a calorie is equal to 4.184 joules. Physicists, however, often deal with extremely small quantities of energy, and so they also measure it with a unit called the electron volt or eV. A kiloelectron volt or keV is equal to 1,000 eV. If you know the energy of a photon or light particle in keV, you can calculate the wavelength with a little algebra. Wavelength is measured either in meters or in billionths of a meter (nanometers).

Instructions

- 1
  Write down the Planck equation, Energy = (Planck constant) x (speed of light / wavelength). The Planck constant is 6.6261 x 10^-34 meters^2 kilograms / seconds, and the speed of light is 2.997 x 10^8 meters / second. Kilograms are abbreviated as kg, meters as m and seconds as s.
- 2
  Multiply the Planck constant by the speed of light to simplify your equation. Your answer will be as follows: Energy = (1.986 x 10^-25 joules m) / wavelength.
- 3
  Convert this number to kiloelectron volts by dividing it by the number of joules per kiloelectron volt, 1.6022 x 10^-16 joules / keV. Your answer will be as follows: Energy = (1.239 x 10^-9 keV m) / wavelength.
- 4
  Rearrange this equation by multiplying both sides by the wavelength then dividing both sides by the energy. This will give you the following: Wavelength = (1.239 x 10^-9 keV m) / Energy.
- 5
  Divide 1.239 x 10^-9 keV m by the energy in keV. If your photon has an energy of 1 keV, for example, your wavelength will be (1.239 x 10^-9 keV m) / 1 keV = 1.239 x 10^-9 meters. This is your wavelength as measured in meters. Note that a more convenient unit for measuring wavelength is the nanometer, which is 1 x 10^-9 meters. You could also report this wavelength as 1.24 nm, which means this photon is an X-ray.

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