So here we're going to solve problem 30 31. The question asks us to plot frequency versus stopping potential. So in order to do that, we're gonna use an equation. But first, let's write down the steps world, um, convert our wavelengths wavelengths. I'll put Omega, as is the symbol for wave links to our frequencies, which is F and we're gonna use an equation that's given tow us. It's assumed that we can use this and that. We know this sees equal to Omega F. I'm sure you know this equation for C is the speed of light, which is three times 10 to the eight meters per second. Um, to get our frequencies, we just rearrange like so f equals to see over mega. Now what? It just so happens that our frequencies, our frequencies, are going to be in the magnitude of the hundreds of trillions hundreds of trillions, which is around, um, the 10 to the 12. 10 to the 14 range. So what I'll do is I'll write the frequencies in, um times 10 to the 12. So whatever number right down, I'll just multiply this. You should assume that it's multiplied by 10 to the 12th. Okay, So in other words, it's gonna be in terror. It's so our frequencies that we get from using the equation from below air and terror hurts. 820 uh, 740 688 6 10 5 50 and 5 18 So now that we've gotten that done, our second step is to graph frequency in the X axis. Monograph are frequency on the X axis and our stopping potential on the Y axis. Okay, so let's draw a graph here. These are axes R F R Frequencies on to be on the X axis are stopping potential on the line. Um, in our data does not start at zero. So all kind of right this mark here to indicate that our frequencies start around 500 By the way, this is five. Whatever number is going to be multiplied by 10 to the 12 hurts, just like how I wrote about. So it's around 500. Terror hurts all the way up to over 800 terrorists. So we'll just go to this for good measure. I stopped in potential goes all the way up to about 1.5 volts. So anything above one point for, well, just plan above there. Okay, so that's plot our data. And now a plot it and I'll speak afterward so that we can go by. I'm fast. But for the 1st 1 actually, I'll just say we have 518. Terror hurts, of course. Mining 2.24 votes for our stopping potential. It's about there Texas 5 50 and points three. Sex. Can we have 6 10 in 100.62 and I'll just go ahead and plot the rest? Right? Okay, so now that we have our Dina plotted, I want you to notice that it's posits sort of positively correlated, and it's linear. So we're gonna use point Slope form, which is our former left for mind. And we're gonna use that with another equation that would skip that's given to us and solve some of the questions. So our third step here is to use an equation that's given to us, and that equation is 38. Question 38.4. That is given. Ah, and of course, Chapter 38. And we're gonna use that with point slope formula. Sorry, guys. so formula. And we all know what point that formula is. It's why equals two M x plus B and equation 38.4, which is given to us, is equal to this. It's e v or E vo, which this is stopping potential equal to the energy of light, which is plank's constant times the frequency of light minus the work function of the material. Now we're gonna have to rearrange this to, um, make this look like point slope form. Um, And to do that, we just divide by e on both sides, which is the charge of an electron, by the way, cancels on that side and you're left with vo you gonna each over e v or sorry h over e times f minus the work function over G. Okay, so you can see that we have are starting potential, which is why F for frequency, which is X and have our slope which we now know our slope, which is M, is equal to H over E. And our intercepts for y intercept is the work function over. Remind us the work function over eat? No, um in order to get the slope all you have to do is pick two points on this graph here and use that equation that you learned back in algebra, which is the difference and why between two points is divided by the difference in X and two points. I won't do that here, but you should know that the value would get for Slope is 4.112 times 10 to the negative. 15 folds over hurts. It's such a small number because our hurt value is so big that's on the bottom now, for be all you have to do is use point slope form. Since you know what I m is, you can pick any point on the graph at which gives you a why and the next value we can you can get be. So be is negative. 1.894 Thanks. Okay, these are the two values that we can use to solver our problem. The first problem is to solve for the threshold frequency. Now, with their equation here, the threshold frequency is I'll write it again. I'll write the equation again. E v o equals to age or things constant times the frequency minus the work function theme. The value of the first hole frequency is when the light has an energy that's exactly equal to the work function. That means the elect the electron on the metal plate of the photo electric experiment just rejects. It doesn't have any remaining energy. This is the energy of the electron show. In other words, were saying that this sign is equal to zero. But if we don't, If we divide uhm zero, which is gonna be this value here if we divided by E. And we get this equation, this is on the B zero videos on a vehicle to zero. So this is what I'm saying here. We're going to say that zero is equal to H over E times frequency. When this work function over E if you multiply both sides by e, you would get, um, you get zero equals stay, Jeff minus the work function, which is the threshold. That's a special frequency with a point and what you get the factual frequency. So, um, how do you fix that? Our question, which asks us about the special frequency, could be solved easily by just writing, like so, If is equal to the work function over e divided by each over e. And we know what these values are from up here. Um, the negative of the work function over he is Be So we're gonna get negative, be here divided by the slope, and they're gonna be over. The slope is equal to 1.894 bolts over 4.112 times tend to be negative. 15 Goencz hurts, and this value is 4.59 times 10 to be negative. 14 her. I'm sorry. Uh, it's positive. 14 because through our hearts is going to be in the hundreds of trillions to very large number. So our special frequency is 4.59 times 10 to the 14 hurts. I'll just erase that. So it's clear. Um, our next question is the threshold freaked out. Wavelength and weaken. Solve that by using the equation that we used above and Step one, which was Sequels to Omega f. Not going to write that again. Um, I'll just write it like this are special frequency and, um, Harold label this thresh just to make it clear that we're doing the threshold. It's just see over if their shoulder frequency. Um, in that value, um, I don't write it all out. Um is 650 53 nano meters as the answer for this question. So next we're supposed to solve for the work function in terms of E V E's. So we know the work function minus the work function over E. This is going to be and B is equal to negative 1.89 four volts. So simply all we have to do is multiply both sides by negative one that cancels the negative and multiply both sides by E. And that cancels the E on the left side. And we're let work we're left with. The work function equals to 1.8 nine uh, TVs. So that one was the simplest one so far. And the last question is fine. The value of plank's constant given the value of E. So our slope, which is M, is equal to H over e. So our H value is equal to I m come e. We know what our slope is. And we know what is the charge of the oven electron. So we write everything all out. We get 4.112 times 10 of the 15 volts over hurts times 1.602 times. Tend to be negative. 19 corms. Yeah, and we get approximate value for Plank's constant, which is six point 59 times 10 to the negative. 34 Jewell seconds. Jewell seconds. Because cool arms can be rearranged. Um, um, to get to me when multiply will buy votes over Hurts to get thes units here. So this values kind of close to the true value. But, um, this is the approximate value that you get when using this equation. So thank you for watching this video. I hope to help. I'll see you in the next one.