Calculate the work function, Φ, of this metal.

Question

When a metal was exposed to photons at a frequency of 1.10 x 10¹⁵s^-1, electrons were emitted with a maximum kinetic energy of 4.00 x 10^-19 J. Calculate the work function, Φ, of this metal.

What is the maximum number of electrons that could be ejected from this metal by a burst of photons (at some other frequency) with a total energy of 4.62×10−7 J?

Answer 1

The work function is a complicated term for a simple phenomenon. When irradiating metal with light (in a classical perspective), conservation of energy is followed. Meaning the energy before and after must be equal. The energy before is the potential energy of the electron (let's call it V) and the energy of the photon (let's call it E). The energy after is the kinetic energy of the electron (let's call it k). The equation is V+E=K. Not all electrons have the same potential energy, but when we are talking about work function we are asking for the lowest potential energy (in magnitude). More specifically, this corresponds to the electrons that are easiest to release (and will have the maximum kinetic energy provided in the problem after being released). So to put the definition shortly, the work function is the energy required to release the electrons that are easiest to release.

To solve this, V=the work function and plug in E and K. E and K can be calculated from equations you likely have already learned. E=hf, where h is Planck's constant and f is the frequency of the light (given). K=0.5mv^2, where m is the mass of the particle (electron here) and v is the speed of said particle. plug them in and solve for V, but make sure your units are correct!

To solve the second part, note that the greatest number of electrons will be released if the energy of each photon is exactly the same as the energy of the work function (otherwise, some of the energy will become kinetic energy afterward and will not be used to release more electrons). if you divide the total energy you put into the system by the work function, that will give you the maximum number of electrons that can be released. Hope this helps!