Light is a unique form of energy in that it displays properties of both particles and waves. The fundamental unit of light that displays this “wave-particle” duality is called a photon. More specifically, photons are wave packets that contain a certain wavelength and frequency as determined by the type of light. The energy of a photon is affected by both of these properties. Therefore, the energy of one mole of photons may be calculated given a known wavelength or frequency.
Identify the wavelength or frequency of beam of light. Wavelength is normally reported in nanometers (nm) and should be converted to meters for energy calculation purposes. It should be noted that it is very easy to convert between frequency and wavelength using the speed of light as the speed of light is equal to the product of the frequency and wavelength. For example, assume light has a given wavelength of 500 nm; convert this measurement to meters by multiplying by 10^-9. Thus, 500 nm is equal to 5.0 x 10^-7 m.
Substitute this value into the equation for the energy of photon. The energy of a photon is equal to the product of the speed of light, or 3.0 x 10^8 m/s, and Planck’s constant, identified as 6.63 x 10^-34, divided by the wavelength. Therefore, using the example problem the energy of a photon would be equal to 3.9 x 10^-19 Joules. Energy of photon = [(speed of light)(Planck’s constant)] / wavelength Energy of photon = [(3.0 x 10^8)(6.63 x 10^-34)] / (5 x 10^-7) = 3.9 x 10^-19 Joules
Multiply this value by Avogadro’s number to identify the energy of one mole of photons. Avogadro’s number identifies the number of molecules or particles in one mole of a particular substance and is equal to 6.02 x 10^23. Therefore, the value calculated in the previous step is the energy of one particle and must be multiplied by Avogadro’s number to identify the energy of one mole. (3.9 x 10^-19)*( 6.02 x 10^23)= 2.3 x 10^5 Joules