 Let's solve a problem on photoelectric effect. When light of frequency 2.42 times 10 to 15 hertz is incident on a metal surface The fastest photo electrons are found to have a kinetic energy of 1.7 electron volt Find the threshold frequency of the metal. Hmm. How do we do this? Whenever I'm dealing with any question on photoelectric effect, I always go back to photoelectric equation Einstein's photoelectric equation because I know You can solve any problem just by understanding that equation. So let's go back Let's quickly recap what the Einstein's photoelectric equation was it said if you have an electron inside a metal and you shine light on it Light which is made of photons then those photons have some energy which we can call E of pH energy of photons and When the electron absorbs that energy it uses it for two things a part of it is used to overcome the work function The work function represents the minimum energy the electron needs to escape the metal And so the photon needs to at least have that much energy. Otherwise, no photoelectric effect is going to happen So if my photon has more than enough energy then part of it is used to overcome the work function And the rest of it goes out as its kinetic energy and The rest of it will come out as the kinetic energy now Not all the electrons are lucky to get this much kinetic energy Most of the electrons will lose a lot of their kinetic energy internally So only very few electrons will come out with this energy and that's why we use the word maximum kinetic energy Because most electrons will have less than this value But anyways if you only consider on those electrons who do not lose energy anywhere in Internally then from energy conservation We can now say the energy of the photon must equal this plus this and that is the Einstein's photoelectric equation the energy of the photon must equal The work function plus the maximum kinetic energy Okay, now that I have this equation now I go back to my question and see what's given and what is asked So we are given the frequency of the incident light and how can I connect this over here? Well, if I know the frequency of the incident light I immediately know the energy of the incident photon from Planck's equation Planck's equation says energy of the photon equals h times f So if I know the frequency, I know the energy of the photon. So this is this can be calculated Okay, then we are given the fastest photo electrons are found to have a kinetic energy of 1.7 electron volt Since this is the kinetic energy of the fastest electrons, this is the K max So that's given to me as well. So this is given to me and this is given as 1.7 electron volt So I know this and I can calculate this therefore. I can find out what the work function is Now, let's see what is asked. We are asked to calculate the threshold frequency That's your frequency. What is that? It is the minimum frequency needed for photoelectric effect. How do we figure that out? Well, the work function gives me the minimum energy for photoelectric effect and again from Planck's equation If I know the minimum energy then to calculate the minimum frequency, I can just use the same thing So if I know this the minimum energy the threshold energy or the work function from that I can calculate the minimum frequency needed and there you go I think I have everything needed and I think I can use this and calculate So why don't you pause the video? Hopefully you're pumped now to solve Why don't you pause the video and see if you can try this yourself first before before we solve it together Alright, so the first thing I'll do is calculate the energy of the photon because once I do that from there I can I can subtract this and calculate the work function and then I can calculate the threshold frequency so energy of the photon from Planck's equation is h times f H is should be usually given in the question But anyways, we can take it to be at seven six point six three times ten to the power minus 34 joule second and the frequency is the frequency is two point four two times ten to the power 15 Hertz and Hertz is one over second one over second is Hertz. So this and this cancels So we had left with Jules, which is the energy now We have two options because the energy over here is also in electron volts We can convert everything into electron volts or we can convert everything into Jules You can do either I prefer to keep it in Jules Because then it'll be slightly slightly less tedious and it'll be easier for me to calculate the threshold frequency You will see what I mean. You will see what I mean. You can convert anything. I'll just I'll just keep it in Jules So let's let's calculate this. Let me bring in my calculator Okay, I have some calculations. It's okay six point six three times two point four two that gives me Sixteen point zero four. I'll just keep it at sixteen. Let's just keep it at sixteen sixteen Point zero four times ten to the power minus thirty four plus fifteen that gives me minus nineteen, right? Yes minus nineteen This is the energy of the photon Now what is the kinetic energy that also let's convert that into Jules? So kinetic energy the maximum kinetic energy is one point seven electron volt How do I convert from electron volt to Jules? Now this can be confusing sometimes I think I should I multiply it with something should I divide it by something well for me the trick is I know E is over here So I just substitute for the value of E the value of E is one point six times ten to the power minus 19 So I just substitute over here. So it's one point seven The value of E is one point six times ten to the minus nineteen coulombs And so I get this as coulomb volt because E is so many coulombs and coulomb volt itself is Jules Remember a volt is work done per charge So coulomb volt becomes Jules. So this is Jules. So so I know I'm on the right track I haven't messed up anything over here. So one point six times one point seven again Let's do that one point six times one one point seven that gives me two point seven two and that is the That is two point seven two is the kinetic energy Minus 19 Jules kinetic energy maximum kinetic energy and from this now I can figure out what the work function is going to be The work function is going to be this minus this and That will be sixteen minus two point seven two. I just use my calculator one more time two point seven two Use me thirteen point two eight thirteen thirteen point two eight times ten to the power minus nineteen Jules and To calculate threshold frequency, I just equate it to H times F naught. So this will be six point six So H times F naught. So F naught would be I can divide by H on both sides So I divide by H So I get H is six point six three times ten to the power minus thirty four Jules second. So finally if I do that, okay one last time from my calculator So I get let's see one Thirteen point two eight divide by six point six three that gives me ooh nice number two Okay, so I get two Times ten to the power minus nineteen plus thirty four that is fifteen And there we go that is my threshold frequency and Just to make sure I do some pulse check I see that the incident frequency is more than the threshold frequency that makes sense Right because if it wasn't the case then I wouldn't have gotten photoelectric effect So it's a good way to check, you know to make sure that I haven't made any mistakes over here If for example if this number was way bigger than this number I know I have made some calculation error or some mistake over here Now the same question could have been asked in so many different ways for example there they could have given us The incident frequency and the threshold frequency and they could have asked. What's the kinetic energy? Same way or they could give us what the kinetic energy is and the threshold frequency is and asked What is the incident wave length or the incident? Frequency same thing you just you use this calculate the incident frequency and then convert it to wavelength And this is why I always say whenever dealing with photoelectric effect numericals go back to basics Einstein's photoelectric equation The Nobel Prize winning equation is all we need to solve these questions