hf = φ + ½mv2maxThe equation is based on the conservation of energy.The energy of a photon E=hf is gained by the electron.A portion of this energy φ the work function is used to break free from the metal.The remainder hf - φ is the maximum possible kinetic energy of the electron as it moves away from the surface.
Example:What is the work function of potassium if green light with a wavelength of 510nm shining on it produces photoelectrons that have a maximum kinetic energy of 0.14eVfrequency f = c ÷ λ= 3 × 108 ÷ 510 × 10-9= 5.9 × 1014 Hzφ = hf - ½mv2max= 6.63 × 10-34 × 5.9 × 1014 - 0.14 × 1.6 × 10-19= 3.91 × 10-19 - 0.22 × 10-19= 3.7 × 10-19 J (about 2.3 eV)
Example:What is the work function of potassium if green light with a wavelength of 510nm shining on it produces photoelectrons that have a maximum kinetic energy of 0.14eVfrequency f = c ÷ λ= 3 × 108 ÷ 510 × 10-9= 5.9 × 1014 Hzφ = hf - ½mv2max= 6.63 × 10-34 × 5.9 × 1014 - 0.14 × 1.6 × 10-19= 3.91 × 10-19 - 0.22 × 10-19= 3.7 × 10-19 J (about 2.3 eV)