In this example, we'll look at the photoelectric effect with regards to the kinetic energy of electrons and the threshold frequency for a metal. Let's look at our problem: when an X-ray photon of wavelength 956 picometers strikes the surface, a certain metal emits an electron with a kinetic energy of 9.35 times 10 to the 4th kilojoules per mole. What is the threshold frequency for the metal to start? We'll need an equation that contains the threshold frequency for the metal. Our equation is the binding energy equals Planck's constant times the threshold frequency for the metal. We know Planck's constant, but we're not given the binding energy of an electron in the metal. So we'll need an equation where we can calculate the binding energy from the other information that's given. We are given the kinetic energy of an electron emitted by the metal and the wavelength of the photon that strikes the surface, causing the photoelectric effect. So the equation that we need is: kinetic energy of that electron equals Planck's constant times the frequency of the photon that strikes the surface minus the binding energy of that electron. In this equation, we know Planck's constant. We're also given the kinetic energy in kilojoules per mole of electrons. However, for this equation, the kinetic energy needs to be in joules per electron. So we'll need to use dimensional analysis to convert from kilojoules per mole of electrons to joules per electron. We can convert out of moles of electrons into electrons using Avogadro's number, which is 6.022 times 10 to the 23rd electrons in 1 mole of electrons. And we can convert into joules from kilojoules using the conversion factor: one thousand joules equals one kilojoule. If we multiply these out, our answer should be 1.553 times 10 to the negative 16 joules per electron. We're not given the frequency of the photon, but we are given the wavelength. So we can use the equation: frequency equals speed of light divided by wavelength. The speed of light is 3 times 10 to the 8th meters per second. And in this equation, our wavelength has to be in meters. So our 956 picometers would be 956 times 10 to the negative 12 meters. If you plug this into your calculator, you should get 3.13 times 10 to the 17th Hertz or 1 over seconds. Now that we have all of the variables we need in the units that we need them in, we can rearrange the equation to solve for the binding energy. Binding energy equals Planck's constant times the frequency of the photon that strikes the metal minus the kinetic energy of the electron that leaves the metal. Plugging in our numbers, we can solve for the binding energy, which should be 5.266 times 10 to the negative 17th joules. Now that we have the binding energy, we can solve for the threshold frequency. Rearranging the equation, we get the threshold frequency equals the binding energy divided by Planck's constant. Plugging in our numbers, we can put this into our calculator and we should get 7.95 times 10 to the 16th Hertz or 1 over seconds.