The Photoelectric Effect

effect if E-M radiation is behaving like lumps or packets of energy being delivered one by one. We call these lumps quanta or photons.Photon EnergyLet’s look at these photons. What determines the amount of energy in each photon?Answer: The energy of a photon, E is given bywhere h = plank’s constant and f = the frequency of the radiation.So the greater the frequency, the greater the energy.Note that can be written as as .So greater values of mean smaller values of energy.OK – so in E-M radiation of one frequency you have all the photons with the same energy. Billions of packets of energy being delivered every second.Photons and ElectronsSo what happens when the photons arrive? Let’s look back at the case of the zinc plate at the start of this section. The photons arrive and interact with (hit !) electrons in the metal. Now here’s a useful rule to follow.Each photon only interacts with one electron.It delivers its energy to the electron and disappears (because it is a packet of pure energy and nothing else.) So the electron now has extra energy. What can it do with it? Well, if it has enough extra energy it can leave the metal atom. Of course that means that only photons delivering enough energy will cause electrons to leave the metal.So only photons above the threshold frequency, fo, will cause photoelectric emission.How come more intense (brighter) radiation doesn’t cause emission?More intense radiation simply means that more packets of energy (photons) are delivered each second. But the energy of each packet is unchanged. So if there wasn’t enough energy to cause photoelectric emission, making it brighter won’t change anything.Does every photon produce a photoelectron?Assuming we’re above the threshold frequency, there are other things to think about when the photon arrives.Photons can easily pass between or even through atoms without hitting (interacting with) an electron. So when they do finally hit an electron, there are a number of possible scenarios.1. The photon hits an electron at the surface of the metal. The electron uses the energy that it has gained to leave the atom and head off to freedom. That’s an easy one.2. The photon hits an electron at the surface of the metal. The electron leaves the atom but heads off deeper into the metal and never manages to escape.3. The photon passes deep into the metal before it hits an electron. The electron leaves the atom and heads towards the surface and escapes!4. The photon passes deep into the metal before it hits an electron. The electron leaves the atom and heads towards the surface but it doesn’t have enough energy to push its way past all the other atoms to get to the surface so it grinds to a halt still inside the metal and never escapes.5. The photon passes deep into the metal before it hits an electron. The electron leaves the atom and heads off in the wrong direction and never escapes.So in fact a very small proportion of the photons that arrive at the metal will cause photoelectrons to be emitted.Einstein’s Photoelectric EquationEinstein looked at the way in which electrons tried to leave the metal. He established that it actually takes energy for an electron to leave the surface of the metal. He called this energy the work function, .He then applied the Conservation of Energy Principle for an electron receiving energy and leaving the metal. Compare energy received and used by the electron at the surface.Energy supplied to the electron = hf (energy from the photon)Energy used by the electron is either: used as work function, , to escape from the surfaceoris left with the electron after it has escaped, in which case it is in the form of Ek.So for each electron at the surface which leaves the metal:Energy supplied = energy usedOr This is Einstein’s Photoelectric Equation.The Ekmax is there because only those electrons on the surface will have the maximum kinetic energy on leaving.Electrons from deep inside which make it to the surface and still have enough energy to escape will have used some energy getting to the surface. These electrons will therefore have less energy left once they are free of the metal and so they will have Ek less than the maximum possible.Notice that if you consider the special case where the energy of the arriving photons is hfo (i.e. the energy of the threshold frequency photons), even the electrons on the surface will only have enough energy to overcome the work function and no more. So once they have escaped they will have no energy left. Their Ek = zero. In this case, the photoelectric equation becomes:This is a useful way of calculating the work function for a material.Also it allows you to rewrite the Photoelectric equation as follows:orPhotoelectric CurrentSet up this circuit.The photons arriving at the metal plate cause photoelectrons to be emitted. The plate is called the “emitter”. Those electrons that cross the gap are collected at the other metal plate – called “the collector”. This flow of electrons across the gap sets up an emf between the plates that causes a current to flow around the rest of the circuit. That’s a photoelectric cell producing a photoelectric current.Stopping Potential, VsSet up this circuit.The emitter gives out electrons. So we call it a cathode.If the emf of the power supply is initially zero, the circuit works just like the one above this. As the supply is turned up, the emitter becomes more positive (because it is connected to the positive terminal of the supply). So electrons leaving it are attracted back towards it. If they leave with enough energy they can overcome this attraction and cross to the collector. If they don’t have enough energy, they can’t cross the gap.By increasing the emf of the supply you can find the pd at which no electrons are able to cross the gap. Even those with the maximum energy, Ekmax, can’t do it.At that point, the energy needed to cross the gap = maximum Ek of the electrons.If you remember, work done moving a charge through a pd is W = QV and in this case charge, Q = e, the charge on an electron,thenUsing this information you can calculate the maximum energy of the photoelectrons emitted from the metal.Rewrite the photoelectric equation (from about 3 screens above this point) asorPlot a graph of the results and you get:Obviously, nothing happens unless you get photons with energy above the threshold value, fo. After that, increasing the frequency of the photons increases the maximum kinetic energy of the photoelectrons so stopping them takes a larger value of stopping potential.The gradient of this graph is . This is one method of calculating h, planck’s constant.