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B) The work function for metallic caesium is 2.14 eV. Calculate the kinetic energy and the speed of the electrons ejected by light of wavelength 250 nm: c) What is ...

Question

B) The work function for metallic caesium is 2.14 eV. Calculate the kinetic energy and the speed of the electrons ejected by light of wavelength 250 nm: c) What is the de Borglie wavelength of this electron?

b) The work function for metallic caesium is 2.14 eV. Calculate the kinetic energy and the speed of the electrons ejected by light of wavelength 250 nm: c) What is the de Borglie wavelength of this electron?



Answers

The work function for caesium atom is $1.9 \mathrm{eV}$. Calculate (a) the threshold wavelength and (b) the threshold frequency of the radiation. If the caesium element is irradiated with a wavelength $500 \mathrm{~nm}$, calculate the kinetic energy and the velocity of the ejected photoelectron.

So for the first part, the use equation twenty seven point five toe calculate the maximum kind of energy according to this equation. Maximum kind of taken entirely a sequel. Do such times the frequency minus the walk function And this we can set equal to the product off the electron charge times the stopping potential or to stopping your village. Now we know that this frequency is Stephen by the speed of light over the Waveland. So we have etc. Over Lambda minus the work function. Well, I need times a stopping built it. So we used is a question to solve for stop importing shin. It is unequal to etc. Over Lambda minus w nods over the target off electrons. Now thousand days we get so the value ofthe etc in electron volts. It is forty electron, four times nanometer, and this has been calculated in previous problems. So she wanted you can look it up over the wavelength. It is for sixty four nine, a reader minus the walk from the work function. Just goingto be to point to it electron volts over the charge ofthe electron. So it's called the see because we have electron volt here so evil. Just cancel out directly. So we not will be. Then he just cancel Louds, which of them? And then we get the potential to be CEO. Point three nine two four Fort or nearly called you your pointy nine goals. This is the value of the stopping voltage. Now for five feet, the calculator to speak from the non militaristic, kinetic energy question. It is okay too. How and the square on DH. They use the maximum kind of dignity, so we Max will then be equal to what? Don't ki max cool but him. And you don't want us back on DH. So you have the kind together t which is e times the stopping potential. So this was just me a single point. This will just crazy of point three nine four electron board because we have walls here on multiplying the charge of electron will just make it in a stronghold. So this times So we have to convert this energy into Jules to find the velocity. So meanwhile, the play Yes. Multiply this over with the mass of the electron Man. One day there's a dollar off the whole thing. Andrei, get this velocity still be three point seven one three times ten to the power five meter per second. Oregon's approximately three point seven time standard, the by five meters per second now comparing it with the velocity with the speed off light. You see that this is nearly equal to see the point serial zero one times the speed of light, which is very less than the speed of light. So we are justified in using the classical definition off kinetic energy over here. So this is the valuable velocity that we need now, for the last part to calculate the deep, ugly Waveland, the EU's equation twenty seven point eight according to this equation that we've lent to sick or tow line constant over the momentum. Now, since we have already justified our use off the classical definition off the energy, we can use the same for momentum. It's a plastic aly momentum is m times the velocity. So this is it. Cueto, the plan constant with six point six three times, tend to the foul line is thirty four two one second for what nine point one, one times ten to the minus thirty is on Katie, which is the mass of the electron find. We use the value ofthe velocity here that we can't connect it. So, Andrea, then solve it and we get this collar off. Waveland, Toby. One point nine six times tang to the bar. Nine meter on nearly going toe. No.

Okay, certain in chapter 37 problem 92 here. So says light of wave link for 24 nanometers falls on a medal which has a work function. 2.28 electron volts R A s How much voltage should be applied to bring the current down to zero. Okay, so we're gonna use it quick in 37 for B to calculate the maximum kinetic energy. And if we set that equal to the product of the stopping voltage in the electron charge, then that's convictable. The that's gonna be the voltage that we need to apply toe completely. Stop this. So how that looks like is we have k Max here and we accept this equal to the folk on energy h f minus the work. This must seek equal e times be not, which is our potential difference. Our dish we re arrange that we could solve for being are as h. F. Mai's work function over e. And this also could be written in terms of the wavelength such as H C over Lambda, minus the work function all over he. So now let's figure this out. So we have 12 40 evey nanometers divided by for 24 nanometers, minus the work function, 2.28 e v. All divided by E. Well, this comes out to being 0.65 easy over a. So these just cancel out and we have 0.65 holes go smooth on the part B. Now Barbie asks, What is the maximum speed of the electrons? Well, first, we're gonna used non relativistic kinetic energy equations. KMAX equal the 1/2 in the square. So this there's longer. The velocity we get out of this is significantly lower than the speed of life, and we can use this classical equation. If it's closer to the speed of light, we're gonna have to go back and update this with relativistic equation. But let's be arranged This when we get it. B is the square root of two K max over them, so we can solve this for the speed and we'll get two times 0.65 Evey uber 9.11 covers 10 to the negative 31 kilograms and to keep everything in a sigh. Units. Let's convert this TV to Jules by multiplying 1.6 times in 18 19 jewels for TV cool so we can plug this. In instance, Weariness I units, weeks an answer out or point Pete times 10 to the five meters per second. And this is quite a bit lower, less than 1% of the speed of light. So we can know our classical approximations is good. Awesome. So lastly, we apart see says, What is the De Broglie waving electrons? Well, H b lame to hear The Debra Lee Ray Link has just h over Pete, which is a church over envy. So we can plug that in 6.63 times 10 to the negative, 34 cool seconds over 9.11 times 10 to the negative, 31 kilograms times 4.8 times 10 to the five meters per second. Awesome. We played all this. Soon we get an answer out, check our interests. I units. Yes, yes and yes. So our answer comes out being one 0.52 times 10 to the negative nine meters or 1.52 Nana leaders. Cool is the interest rate

Here a light is incident on a metal with a given work function. And we have to find out maximum kinetic energy of the emitted electrons stopping potential and the maximum speed of emitted photo plans. Maximum kinetic energy is kmax equal to energy of light, which is H F minus work function. It is blanks, constant FS frequency and work. Conscience is an electron world. So we will convert it into jewel by multiplying it by 1.6: 10 to the Power -19. Now this will give us maximum kinetic energy as 5.5 into 10. to the power -20 jules. No. To convert it into electron world, We divided by 1.6 into 10 to the Power -19. This gives us 0.34 Electron Hole. So we have found the maximum kinetic energy both in jewel and electron words for part B. We have to find the stopping potential. So the relation between maximum kinetic energy and stopping potential is came X equal to E. We not we're not stopping potential came at 5.5 into 10 to the power -20 jewels. He is magnitude of charge on a clone. And we're not stopping potential. So this gives that we're not equal to 0.34. Well now for the part C we have to find out maximum speed of the emitted electrons. Maximum speed will be related to like some kinetic energy. We put the values. Mhm. Mhm. Yeah, him is massive, electron v max is max speed. This gives us be Mexico too 347 into 10 to the power fire meter per second in kilometer per second. This will be 3.47 and 2 10 to the bar five upon 1000 kilometer per second, which gives us 347 kilometers per second. So this completes the solution. Thank you.

So in this exercise will have a surface off obedient and we're given that it's working. Work function is to 0.16 election votes, okay, And then were given a certain incident Radiation whose wavelength is feel 113 nano meters. And the first thing we're were asked in question A is what is the maximum kinetic energy off the immediate elections. So we know from the photo electric ah, formula that the maximum kinetic energy ke m is that is h m sorry, it's gonna be age half f is the frequency. Mine is the work function now since we know that the frequency can be redness the speed of light over Lunda, then k m maybe reading us HC over Lunda minus the work function. And I always think you have to blow in the numbers. HC is 1240 electing votes never meters. So here have 1240 over 413 and a meters minus 2.16. And this, um is no 0.84 electoral votes. That's the in search of question eight. Okay, and then question be asks us. What is the threshold wavelength for the surface so the threshold wavelength will happen when the kinetic energy off the emitted electrons is zero. And for that to happen, we gotta have HC over Lambda equals to the work function and then isolating the work function we have the, uh I'm sorry, isolating the London we have Lambda equals H C over the work function, which is 1240 electoral votes nanometers. If I don't wait to 0.16 and this is 574.1 millimeters and this is the answer to question be


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