 Hi, I'm Zor. Welcome to Inizor Education. Today I will solve, well, a couple of problems. It's not really problems. It's basically exercise and calculations related to effect of photoemission. Now, this is a continuation of previous two lectures where these effects of light, when light, let's say, hits the surface of metal, whatever, silver for example, it can basically kicks off electrons. Now, this is a photo effect. It's a photoelectricity when electrons are kicked off. Now, we were talking about certain approaches, how to explain this particular effect. Now, we came to basically an explanation which was offered in 1905 by Albert Einstein, which in turn was based on certain propositions Max Planck did at the end of the 19th century, like there were 10-15 years before that. And it's all related to principle of electromagnetic waves delivering energy not as a continuous process, continuous in the mathematical view, which means it can be subdivided into as small pieces as possible. Apparently, that's not the case. Apparently, there is something which is the minimum of energy and below this you cannot really deliver that energy, smaller than that minimum. And that minimum depends on the frequency of oscillations, basically. Now, it's kind of approach to quantum mechanics, the quantum theory, and I'm not going to go into all the details of this. I would like to stop actually where we are, that the energy by electromagnetic field is delivered in certain pieces, photons, quantum, if you wish, quantum of energy, which is called photon. That apparently explained a lot of different effects related to photoelectricity suggested, these all explanations suggested by Einstein, which he received Nobel Prize many years after, like 17 years after he actually published this article. And it was related to the fact that classic electromagnetic theory based on Maxwell's equation is really based on assumption of continuity, that it really is unbroken kind of thing. It's just waves basically in their classical viewpoint, like waves on the surface of the sea. Now, quantum approach which suggested by Einstein was so much different because it actually went back to Newtonian corpuscular theory of light, that the light were just individual particles. So it went basically, at least philosophically, to that particular side. And that's why this explanation offered by Einstein was kind of met with skepticism, let's put it this way. But nevertheless, eventually his opinion basically won sufficient amount of support and sufficient amount of experiments were conducted and eventually it was really confirmed. So these couple of exercises, which I will do, I will based on that particular approach. Now, whenever electron is circulating around the nucleus, that's our classic model. Well, we can call it that it actually goes in orbit, a little bit more correct name actually related to the fact that this is in three-dimensional world. So we can say that electron occupies the place somewhere in a shell of certain radius. So this shell is characterized by certain amount of energy needed to kick this electron out from the attraction of the nucleus, the protons in the nucleus actually. So while electron is at certain distance, there are obviously forces, electron is negative, proton in the nucleus is positive, they attract each other and it all depends basically on the distance between them and probably many other factors. But whatever it is, there is definitely attraction which keeps electron within that shell. Now, whenever the electromagnetic waves, like light for example, hit the surface of, let's say metal, like silver plate for example, it needs this energy to kick off the electrons from their shell around the nucleus. And we were talking about in previous lecture some kind of, well, common sense explanation why higher frequency of light kind of expects to kick stronger, so to speak. And we basically came to an equation. If you need a certain level of energy, E, I will call it binding. This is energy which is necessary to kick off electron from the shell where it's circulating around the nucleus. Now, this energy should be supplied by the light by electromagnetic field and each photon is possessing energy equal to Planck's constant and frequency of the light. So, the higher frequency of the light, the higher energy this particular photon of that particular light possess. Now, as I was saying before, the quantum theory actually assumes that this energy is supplied in individual packets if you wish, or quantum or of energy or photons and it's supposed to be consumed by electron to excite it and it needs to do something with this energy and it flies away. If the energy is greater than this, the fly away electron has more kinetic energy after it broke its relationship with the nucleus of the atom. So, basically it's supposed to be this for photoelectric effect to take place. So, for each electron or rather all electrons which are sharing the same shell around the nucleus, this binding energy exists in some way. I mean, it's measured somehow. There are certain experiments and this is an energy of one quantum which light electromagnetic waves possess. And as long as it's greater than we have this effect of photoelectricity. Now, my first problem is basically very simple. I have to determine all the light characteristics like frequency, angular frequency, wavelengths and the period if I know the binding energy of specific electron or electrons in a specific shell. Well, minimum obviously, whenever there is a quality here. So, the quality means that this is minimum. So, I would like to find this minimum frequency if I know this one. Well, this is a simple exercise obviously and let's just do it very simple. So, F minimum is equal to the binding energy divided by Planck's constant. Simple enough. Now, other characteristics of that particular light. So, we know the frequency. So, what is let's say the period tau? Well, period is 1 over F, right? So, the period is equal to H over E binding, right? So, the greater the frequency, the smaller the period. So, if minimum, if this is minimum, this is actually maximum. So, what is the maximum period of the wave falling on the surface of whatever, the metal or whatever, needed to keep of electrons if energy of binding is given. Now, what's next? Next is the wavelengths, lambda. Now, what is the wavelengths? Wavelength is speed of light times period, right? Speed times times gives you distance and period is just one wave. So, this is the length of one wave from which we derive that this is C times H divided by E binding. What else do we need? Angular period is 2 pi times F, right? Because every circle, every oscillation is 2 pi in angular frequency. So, omega is equal to 2 pi times E binding divided by Planck's constant. So, this is kind of a, it's not really the problem, it's kind of an exercise basically on algebraic manipulation with numbers. But this is the most important part. So, whenever your quantum of energy supplies certain amount of energy, which is at least equal to this one, if we know this one, we can determine what kind of light is needed. And the second problem is to apply basically all this information to a concrete case. So, concrete case is E binding is equal to 5.17 electron volt. Okay. And we have to do basically all the calculations with this particular example. Now, and the first most important part, what is electron volt? Well, electron volt is also a unit of energy. Like JOL. JOL is a seized unit, a system of international unit of work of energy. Now, electron volt is just another and we have to somehow convert it into JOLs. Now, what is electron volt? Electron volt is energy needed for one electron to move between potentials of one volt. So, how much energy we need to move electron between two levels of energy differences in their voltage is one volt. Okay. Now, let's recall what is voltage. Voltage is amount of energy needed for one cologne to go from one place to another. Remember this, right? So, if the voltage is one volt and I'm moving one electron, all I need to do is convert the electrons charge into coulons or express electrons charge in coulons and multiplication of coulons by volt gives me amount of work which is needed, right? So, the voltage is one volt, so that's simple. So, I need to know the charge of electron times voltage between two pieces which is one volt and that would equal to amount of work. So, all I need is to know what's the charge of electron in coulons and this is given. So, let me just give it to you as condition. Electrons charge is equal to 1.602 blah, blah, blah. Now, more numbers I have in the notes for this lecture times 10 to which degree? Minus 19 coulons. And also we need h which is Planck's constant which is 6.626 10 minus 34 and the units are meter square kilogram second. So, this is given. Now, based on this, I can say that one electron volt is equal to charge times difference in potential, difference in potential, electric potential is one volt. So, it's basically 1.602 times 10 to the minus 19 joules coulon times volt, that's joule. Okay? So, we got this. And we have 5.17 electron volts. So, we have to multiply this by 5.17 and the result would be and the result would be here 8.282 times 10 to minus 19 joules. Okay. Now, we know h that's 6.626. So, it's 6.626 times 10 minus 34, the f minimum. So, from here we can get f minimum by dividing the energy. 8. something 10 minus 19 divided by 6. something 10 to the minus 34. So, we can find this one. And this is equal to 1.25 times 10 to which degree? 15. Now, let's talk about units. Okay. So, units is joule divided by this one, which is the Planck constant, which is meter square kilogram and second goes here. Now, what is joule? Joule is its work. So, it's force times distance. So, it's Newton times distance meters. Now, what is Newton? Newton is the force and the force is kilogram meter divided by second square. Right? Kilogram times meter, mass times acceleration. This is a mass and this is acceleration. f equals to m times a, remember? So, what's the result? m and m is square and 1 second. So, the result is 1 over second, which is actually correct unit for frequency. How many oscillations per second? So, we have correct dimension, correct units, which is very important. We have to check the units all the time, obviously. Okay. From which we can find out the period, which is inverse of this, which would be 1 over 1.25 times 10 to the minus 15 seconds. That's the period. Now, lambda, the wavelength is speed of light, which is 3 times 10 to the 8th meter times this. So, we have to divide it by 125, 10 minus 15. This is meter per second, I'm sorry. And now, this is second. So, seconds go out and we have 3 divided by 125, which is what? 2.4. So, it's 2.4 times 10 to minus 7, right? 8 minus 15 meter. Well, when light is concerned, we usually do it in nanometers. Nanometers is 1 nanometer 10 to the minus 9 of a meter. So, this is equal to, I have to multiply this at 100 and divide it by 100. So, it would be 10 minus 9 and this would be 2.4 nanometers. Now, 2.4 nanometers. Now, the visible light is from about 400 nanometers to 700 nanometers. So, this is shorter than the shortest visible light. Shortest visible light is what, like, violet or something like this. This is ultraviolet. So, whenever ultraviolet light. Now, these are, by the way, the real numbers. And I started from certain energy, binding energy for, what was it, 5.7 electron volt. I think I took it from the gold. So, if we have a plate of gold, then electrons can be, well, there are certain orbits, certain shells, which possess this particular binding energy. So, for gold, you need ultraviolet light of lengths, wavelengths of 240 nanometers to start kicking the electron. And if I will increase intensity of this light retaining the frequency, I will have more electrons, but the energy of each electron as it comes out would be exactly the same and it's defined by the frequency. So, the frequency defines energy, kinetic energy of each electron. The intensity of the light, well, amplitude of light of oscillations, amplitude, defines basically the number of electrons kicked out from the surface. So, these are two kind of exercises. I don't want to say the problems. And I suggested to read the notes for this lecture on Unisore.com. Unisore.com called the Physics 14 course. So, notes contain basically exact numbers. Here I just approximated as far as I know. Well, basically that's it. That kind of concludes my photoelectricity part of certain characteristics of light. And there are some others which we will address in the next lectures. Thank you very much and good luck.