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### Course: Modern Physics (Essentials) - Class 12th>Unit 2

Lesson 3: Einstein's elegant equation to decode the photoelectric effect

# Calculate threshold frequency

When light of frequency 2.42 X 10^15 Hz is incident on a metal surface, the fastest photoelectrons are found to have a kinetic energy of 1.7eV. Find the threshold frequency of the metal. Let's explore how to use Einstein's photoelectric equation to solve such numerical on photoelectric effect. Created by Mahesh Shenoy.

## Want to join the conversation?

• omg thankyou its so easy
(1 vote)
• how come the frequency f change to f naught? like do you mean to say light comes with a frequency f but changes to f naught on hitting the electron?
(1 vote)
• The frequency of light doesn't change. Every type of energy has some frequency (E=hf). Now, when the light hits the metal surface, say E1=hf1 energy was required to Knock the electrons loose. The rest E-E1 will go into the kinetic energy of electrons. That f1 above is what we call f naught. See, the frequency didn't change. Think of it like some frequency was spent in electron ejection and some went into kinetic energy.
Hope it Helps :)
(1 vote)

## Video transcript

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 photoelectrons are found to have a kinetic energy of 1.7 electron volt find the threshold frequency of the metal 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 photographic 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 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 thanks 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're given the fastest photoelectrons 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 threshold 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 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 all right 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 pressure 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 it's around 6.63 times 10 to the power minus 34 joule second and the frequency is the frequency is 2.42 times 10 to the power 15 hertz and hertz is one over second one over second is hertz so this and this cancels so we are left with joules 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 joules you can do either i prefer to keep it in joules because then it will be slightly slightly less tedious and it'll be easier for me to calculate the threshold frequency you will see what i mean you'll see what i mean you can convert anything i'll just i'll just keep it in joules so let's let's calculate this let me bring in my calculator okay i have some calculations okay 6.63 times 2.42 that gives me 16.04 i'll just keep it as 16 let's just keep it at 16. 16.04 times 10 to the power minus 34 plus 15 that gives me minus 19 right yes minus 19. this is the energy of the photon now what is the kinetic energy that also let's convert that into joules so kinetic energy the maximum kinetic energy is 1.7 electron volt how do i convert from electron volt to joules and this can be confusing sometimes i think or 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 1.6 times 10 to the power minus 19. so just substitute over here so it's 1.7 the value of e is 1.6 times 10 to the minus 19 coulombs and so i get this as coulomb volt because e is so many coulombs and coulomb volt itself is joules remember uh volt is work done per charge so coulomb world becomes joules so this is used so so i know i'm on the right track i haven't messed up anything over here so 1.6 times 1.7 okay let's do that 1.6 times 1 1.7 that gives me 2.72 and that is the that is 2.72 is the kinetic energy minus 19 joules 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 16 minus 2.7 to just use my calculator one more time 2.72 gives me 13.28 13 13.28 times 10 to the power minus 19 joules and to calculate threshold frequency i just equate it to h times f naught so this will be 6.6 so h times f naught so f naught would be i can divide by h on both sides so divide by h so i get h is 6.63 times 10 to the power minus 34 joules second and so finally if i do that okay one last time for my calculator so i get let's see 1 13.28 divided by 6.63 that gives me oh nice number two okay so i get 2 times 10 to the power minus 19 plus 34 that is 15 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 made some calculation error or some mistake over here now the same question could have been asked in so many different ways for example 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 frequencies and asked what is the incident wavelength or the incident frequency same thing you just you you use this calculate the incident frequency and then convert it to wavelength and this is why i always say whenever dealing with photoelectric equat effect numericals go back to basics einstein's photoelectric equation the nobel prize winning equation is all we need to solve these questions