All photoelectric effect graphs: Effect of intensity/frequency

in this video we're gonna change the brightness and the color of the light or the intensity and the frequency of the light and see how that affects the graph of the photoelectric effect and the reason i have two graphs is because we'll do two cases now before we start let's quickly recap what this graph was all about on the horizontal we have plotted the voltage of the collector plate and on the vertical we are plotting the current over here now when the voltage of the collector plate is positive and it's increasing it starts attracting more and more electrons and as a result it starts collecting more and more electrons and as a result the current starts increasing but after a point it's collecting all the electrons that are emitted and then further increasing the voltage does not increase the current and that's why we hit a saturation and so we saw that this is an indicator this current the saturation current is a direct indicator of how many electrons are coming out per second so i'll just say hash for number of photoelectrons we call them this is the number of photo electrons coming out per second you can think of this height represents this number and then when we make the voltage on the collector negative by say flipping the battery now the collector starts repelling the electrons and so electrons start going back and as a result the current starts reducing reducing in eventually eventually it stops and we know at this point even the fastest electron the most energetic electrons have also stopped they're not able to make it and therefore this point is what we call this voltage this negative voltage is what we call the stopping voltage or the stopping potential and this is a direct indicator in fact it's equal to in electron volts the maximum kinetic energy and if you need a refresher on this and we've talked a lot about this in our previous video so feel free to go back and check that out but now what we'll do is let's change the intensity and the frequency in the first case i'm going to increase or let's say i'm going to decrease i'm going to decrease the intensity of the light but i'm going to keep the frequency of the light the same and i want us to predict what the new graph is going to look like and i think we've already learned everything that is needed we've already seen how the intensity and the frequency affect the number of photoelectrons and affects the maximum kinetic energy now all we have to do is use that and translate it into drawing what the new graphic is going to look like so a great idea to pause the video and see if you can try doing it yourself first all right let's do this so let's start with the frequency part since the frequency is staying the same that means the energy of my photons are going to stay the same so whatever was the energy of that my photons were that has not changed why because remember planck's equation is equal to h into f and so if the energy of the photons have not changed that means the energy that we're giving to the electrons have not changed that means the energy with which the electrons are coming out that won't change and so the maximum kinetic energy will stay the same so i know that my graph is going to end over here it has to i'm going to draw my new graph with green it has to be over here okay now let's look at what happens over here and that's that's all we have to do we have to look at these two things how these two things changes now let's look at the what happens to this one for that let's look at the intensity so when i reduce my intensity what happens well as i reduce the intensity the number of photons that reduces so i'm reducing the number of photons that are falling on this per second and if that reduces the number of electrons coming out would reduce and that means this current should also reduce and therefore i know that my saturation current my maximum current has to be smaller because now the less number of photoelectrons are coming out and therefore now i can predict what the graph is going to look like it's going to be similar to this but now my graph will look somewhat like this and there we go all right okay now you try one in the second case let's get a little bit more adventurous let's increase the intensity of light let's make this light brighter but let's decrease the frequency okay can you now predict what the new graph is going to look like pause and try all right again maybe let's start with the effect of frequency if the frequency has become smaller then now i know from planck's equation the energy of the photons should have also become smaller so these photons have now become very tight very tiny i mean tiny as in like tiny energy okay they don't have size or anything they become they have less energy now and since they have less energy they transfer less energy to the electrons and therefore the electrons will now come out with less energy therefore the maximum energy of the electrons would be smaller and therefore the stopping voltage would be also smaller so i know in this case the stopping voltage has to become smaller and when i was telling this i should try to directly memorize if frequency decreases stopping voltage would reduce if intensity happen increases this happens that happens that's very boring it can be very confusing so please don't do that instead always go back to your basics frequency decreases that means the energy of the photons reduced that means less energy is given to the electrons and therefore it will be easier to stop them and therefore smaller stopping voltage all right now what happens due to the increased intensity well if the increased intensity has increased remember intensity is an indicator of how many photons are there per second more intensity means you're getting more photons per second right and if there are more photons per second there'll be more electrons coming out per second and if there are more electrons coming out per second that means the saturation current should be higher so i know that in this case the saturation current should become larger and so now i can predict the graph should go from here to here the graph has to stick similar to this so it's going to go like this maybe and then isn't it fun to do this logically okay because we're having so much fun let's do two more bonus graphs in this graph we're going to plot the stopping voltage along the vertical so not the voltage of the collector but the stopping voltage itself versus the intensity of light okay i want you to predict what this graph is going to look like provided we keep the frequency same so we're going to keep the frequency constant so think about what this graph means what we're doing with the light and then predict what this graph is going to look like so again beautiful idea to i'm sorry i'm getting ready to pause and see if you can try this okay first step is try and figure out what we are trying to do over here we are changing the intensity right so we're keeping the frequency the same and we are making it brighter imagine that we are increasing the brightness our question is what happens to the stopping voltage or in other words we are asking what happens to the maximum kinetic energy of the electrons what do you think is going to happen well as i increase the intensity i'm increasing the number of photons right but the energy of each photon stays the same because the frequency is a constant planck's equation e is equal to hf and therefore if the frequency stays the same that means the energy of the electrons coming out stays the same right it's exactly this graph right i changed the intensity but the the stopping voltage did not change so if i change the intensity the stopping voltage will not change so it's all about just getting what it's looking i mean taking what we have already learned and putting into a graph so whatever was the stopping voltage earlier i don't know what that was so let's say the stopping voltage earlier was i don't know maybe three volt then here throughout the stopping voltage will stay three volt that means our graph is going to look like this so let me use okay let me use yellow itself is going to look like this makes sense okay one last one last graph what if i draw a graph of this time again stopping voltage versus frequency okay keeping intensity the same i'm not going to change the intensity all right if i increase the frequency of the light that means i'm increasing the energy of the photon planck's equation is equal to hf so if the energy of the photon is increasing that means the kinetic energy of the electrons will also increase that means the maximum kinetic energy will increase that means the stopping voltage should also increase so we know as the frequency increases the stopping voltage will increase but is it going to be a straight line is it going to start from 0 is it going to be a curve how do i how do i figure that out so that's why this part is a little tricky maybe a little bit more interesting for that we can go back to our equation there's only one equation that we have for photoelectric effect that's einstein's equation einstein's equation says that the energy of the photon which i'll just write as h times f and this is our frequency on the x-axis that should equal the work function which is a constant plus the maximum kinetic energy which is basically the stopping voltage right and what i see is a direct linear relationship and therefore i know it has to be a straight line but does that straight line start from zero think about it what do you think the straight line can't start from zero because if the frequency is too low then it's not able to overcome the work function we will not have any kinetic energy we will not have any stopping voltage so the frequency will if the frequency is zero nothing happens if the frequency is little higher again nothing happens right so if you start with very low frequency you get no photoelectric effects so stopping voltage should also be zero until you hit that minimum threshold frequency maybe somewhere over here after that if you now increase the frequency now the this one the maximum kinetic energy would increase dropping voltage would increase and so now there will be a linear relationship so now it'll increase linearly so it's going to be a straight line somewhat like this and there we go this is what the graph would look like