Stopping potential & maximum kinetic energy

in photoelectric experiments we are always interested in finding two things one is counting the number of electrons coming out per second something that we discussed in our previous video and the second which we'll discuss in this video is calculating or measuring the maximum kinetic energy of the electrons so the question is how do you find what is the maximum energy with which these electrons are coming out i find it even fascinating that we can even perform experiments to do that now just to quickly recap we've already seen the experimental setup we used to count the number of electrons emitted per second the whole idea was the number of electrons collected per second must be a direct indicator of the current the current directly indicates how many electrons were collected per second but that did not necessarily mean the may not necessarily be the same as the number emitted per second because some electrons can be lost not all electrons will be collected and so then we attached a battery to ensure the collector can suck all the electrons and we realize that as we increase the voltage this current starts increasing and eventually it maxes out when the current has reached maximum that's when i know for sure that all the emitted electrons almost all the limited electrons must be getting collected because the current is not increasing anymore and that current and we draw a graph we draw a graph of the voltage of the collector versus this current the current over here and we found that once the current reaches maximum that current is a direct indicator we call that as the saturation current or the max current is a direct indicator of how many electrons are coming out per second and we've discussed this in detail in our previous videos so feel free to go back and check that out if you need a refresher but can we use this setup to somehow figure out with what energies or what kinetic energies are these electrons coming or think about measuring how fast these electrons are moving how do we do that well the trick is you try and stop these electrons think about it if it takes very little effort to stop these electrons that means the electrons must be moving very slowly they must have they must be having small kinetic energy but if it takes a lot of effort to stop these electrons then they must be having a very high kinetic energy so the whole idea is you try and stop these electrons now the question is how do we how do we stop these electrons and how do we figure out how much effort it takes to stop the electrons i want you to think about it in this situation the collector is connected to the positive so the collector is attracting the electrons now if you want to stop this electron what should you do what change can you do in this experiment can you pause the video and think about it all right so i want my collector to try and stop the electrons right that means i need my collector to repel the electrons this time if i want to make the collector repel the electrons that means my collector should be connected to the negative terminal of the battery oh so i have to just flip the battery that's the modification i need to do all right so let's do that let me flip the battery so i put negative terminal to the collector put positive over here so now i'm giving negative voltage to my collector so now let's think about what's going to happen to our current well when there was no battery there was some current because there were some of you know some photoelectrons were reaching the collector and as a result there was a current even without the battery but now since i've given a negative voltage to the collector some of these electrons which are reaching earlier they will now stop reaching they'll get repelled and maybe they'll turn back maybe this electron will also stop and turn back but not all maybe these electrons have very high energy so they're slowing down but they don't stop slowing down but they don't stop and they still get collected so will still get a current but the current will now become a little smaller because some electrons are turning back and since our goal is to find the maximum kinetic energy and kinetic energy of the fastest electrons we should try and stop the fastest electrons so maybe enough put say one volt negative one volt but let's say i put one volt and at one volt the current is still there so what will i do i'll say hey one volt is not enough to stop my electrons i will increase it maybe i'll increase it to two volts and maybe now i find that some more electrons maybe this electron will also turn back if this electron will also slow down stop and turn back but maybe this electron oh this electron is still very powerful slows down slows down but it doesn't turn back it's still getting collected so even at two volt i get a small current but there is a current the fastest electrons are not stopped yet so now i just increase the voltage i keep on increasing the voltage the current keeps on decreasing but the fastest electrons are still making it eventually let's say i go to 2.9 volt let's say at 2.9 volt i still get a current that means let's say this is the fastest electron it is slowing down slowing down but it's still reaching and so i'm getting a current so now let's say i increase from 2.9 volt to 3 volt and at 3 volt i find my current goes to 0. what does that mean that means at three volt and i'm taking simple numbers over here so that is easy for us to understand at three volt this fastest electron must be coming all the way till here all the way till here and must be stopping and turning back how do i know it stops here because i know that 2.9 volt it was still making it so at 3 volt it must have stopped now if i increase the voltage further the current will stay zero and so i now know that it takes 3 volts to stop my electrons and this now is an indicator of how energetic the electrons are now imagine if in another photoelectric experiment it took me 10 volts to stop the electrons ah now i know over there electron the maximum kinetic energy must be much higher you get that so this voltage which we call the stopping voltage the voltage that is needed to just stop the photoelectric effect is a direct indicator so let me write that so the kinetic energy maximum can be directly found out by finding can be measured by finding the stopping voltage stopping voltage is the minimum voltage needed to stop the photoelectric effect and get this not only is there a direct correlation between them if you know the stopping voltage you can actually find out what is the maximum kinetic energy of these electrons yeah and we'll do that in a second but before we do that i want you to complete this graph okay so now we're on this side of the graph because we are putting a negative voltage to our collector so i want you to think about what would that graph look like as i increase the voltage in the negative side so can you pause and try and complete that graph well all right so we know as i increase the voltage in the opposite direction giving negative voltage the current becomes smaller and smaller and eventually goes to zero so i know the graph should somehow go to zero all right so it turns out the graph goes to zero somewhat like this and this point at which the current just stops the minimum voltage needed to stop the current that is our stopping voltage and in our example we took that as three volt all right now let's come to the last part given the stopping potential can we actually tell how much kinetic energy this fastest electron had the answer is yes but how well one way is to use equations and do it and i find that dull and boring another way is to do it logically i first ask myself this question what does it mean when i say the potential difference here is 3 volt what is the meaning of that statement potential difference is an indicator of how much energy a charge is gaining or losing when it moves from one point to another so when i say three volt it means a charge when it goes through that three volts gains or loses three joules of energy per coulomb that's the meaning of this that's the meaning of potential difference so this fastest electron has lost three joules of energy per coulomb but since the final energy is zero that means it must have had three joules of coulomb to begin with and so that means the kinetic energy of the electron and this is the fastest electron must have been three joules per coulomb to begin with now you might say what is the meaning of that three joules per coulomb to begin what is the meaning of that well this means that if electron had one coulomb of charge then its kinetic energy would have been three joules if electron had two coulombs of charge then its kinetic energy would be three joules times two if the electron had ten coulombs of charge then the kinetic energy would have been three times ten but we know how much charge an electron has an electron has 1.6 times 10 to the power minus 19 coulombs of charge and therefore its kinetic energy must be three times this number and there we go we have now measured the kinetic energy of the fastest electrons that that was there in this experiment and of course you can calculate that the coulomb cancels 16 3's are 48 so this would be 4.8 times 10 to the power minus 19 joules isn't this mind-blowing that we can perform an experiment and find out the kinetic energies of electrons oh my god i can't believe this that we can do the experiments like these but anyways remember we can only do that for the fastest electron because if you take some other electrons i can't do that because these electrons did not travel the entire three volt so this electron must have traveled only for two volts before turning back this electron must have been stopped maybe just by one volt and therefore this is the energy of only the fastest electrons so this is the maximum kinetic energy okay now last thing is because these energies are so tiny instead of writing it in joules we can write it another way the another unit and the way to think about this is we'll write 3 and instead of writing instead of substituting the value of e we'll just call that as e we'll just keep it as e so we'll keep this as e and so what remains is just joules per coulomb which is volt 3 electron volt and so we can just say hey the maximum kinetic energy in this experiment is 3 electron volt and what you see is that's the same as the stopping voltage so if the stopping voltage was 10 volt i immediately know the maximum kinetic energy in that experiment must have been 10 electron volt and if you want to convert it to joules just substitute for e multiply and you'll get in joules incredible isn't it so long story short you if you want to calculate the stopping maximum kinetic energy you basically find out what's the stopping voltage and the stopping voltage itself equals the maximum kinetic energy but in electron volts if you want in joules then you just multiply that number with 1.6 and 10 power minus 19 and you will get that so putting it all together if you want to count how many electrons are emitted per second then that is indicated by the saturation current and if you want to count what is the maximum kinetic energy with which these electrons are coming out that is indicated by the stopping voltage and now we can play with this we can change the intensity of light change the frequency of light and based on what happens to the saturation current and based on what happens to the stopping voltage we can now tell what's happening to the number of electrons coming out per second and what's happening to the maximum kinetic energies of these electrons