Light with a frequency of 200nm is shone on a sodium plate with a work function of 2.28eV and electrons start escaping the surface of the plate due to the photoelectric effect. What is the maximum kinetic energy of one of these electrons in eV?
The work function of a metal is the minimum amount of energy required for electrons to start escaping the surface. This means that if we calculate the energy of each photon from the light and subtract the work function we might be left over with some energy that would be transferred to the kinetic energy of the electron. The equation we will need is this: Ek (max kinetic energy) = h (planck constant) * f (frequency of photon) - w (work function)
h*f is equal to the energy of the photon
The frequency of the photon can be found using the wave equation: frequency = velocity/wavelength where the velocity is the speed of light (3.00 x 108). This gives us a frequency of 1.5 x 1015 Hz.
Planck's constant is 6.63 x 10-34 Js. But be careful with units here as we need the energy in eV, not Joules. So to convert our answer for the energy of the photon we must divide it by the charge of an electron (1.60 x 10-19 C).
Calculating the energy of the photon gives us a value of 6.21 eV.
Then to get the maximum kinetic energy of the electron:
Ek = 6.21 - 2.28 = 3.93 eV (to 3 significant figures as that is what we are given in the question)
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