Photoelectric Effect Theory Lesson

the photoelectric effect and the particle nature of light before we can study the photoelectric effect we need to look at the electromagnetic spectrum there's some facts that you really need to know very well the electromagnetic spectrum is made up of seven parts from gamma rays right down to radio waves so the highest frequency electromagnetic waves are the gamma rays they go from gamma rays to x-rays in ultraviolet then a small section is our visible light infrared microwaves and radio waves radio waves have the longest wavelength gamma waves have the shortest wavelength the shorter the wavelength the higher the frequency the longer the wavelength the lower the frequency all of these waves are transverse waves they all travel at 3 times 10 to the 8 meters per second this value is given to you on your data sheet they can all travel through a vacuum they don't need any mechanical particles to move and they all obey the wave equation where we can say V for speed is frequency times wavelengths but when we speak about electromagnetic waves we can use a C in the place of the V we see is 3 times 10 to the 8th meters per second as mentioned over there electromagnetic waves carry energy in packages and we call these packages of photons think of photo which has to do with light the energy of the photons is dependent on the frequency of the electromagnetic waves and as you can remember from the previous sketch that we had gamma rays had the highest frequency so the photons would have the highest energy it's all according to this equation this is the energy of your photons of your electromagnetic waves so the higher the frequency the higher the energy H is Planck's constant 6.6 3 times 10 to the negative 34 joules times seconds remember it's not joules per second or you can give the equation as Planck's constant times the speed of electromagnetic waves by the wavelength because frequency is equal to speed divided by wavelength the higher the frequency of the photons the greater the energy of the photons the more the photons will behave like particles if they have high frequency so obviously then gamma rays which have the highest frequency of all electromagnetic waves will have the highest energy and they will behave the most like particles if we take this equation and we make our constant a 1 the equal sign becomes a proportionality so energy of your photons is directly proportional to the frequency of the photons they can ask you to draw the graph for this it is normally not in your textbooks or it will be one of the options for a multiple choice question so frequency of your photons determines the energy of the photons it's a direct proportionality therefore it is a straight line graph through the origin so I've used x-rays as an example there the second highest section of on our range of electromagnetic waves after gamma rays x-rays with a very high frequency have more particle nature than wave nature because they have high energy the higher the energy of the photons the more they're behave like particles we are now going to look at the relationship between the energy of the photons and the wavelength of the electromagnetic waves if you remember again gamma rays are on the left-hand side of the sketch so they have the shortest wavelength the shorter the wavelength the greater the energy of the photons it comes from this equation H is Planck's constant C is the speed of all electromagnetic waves these two values are constants make them a 1 and your equal sign becomes a proportionality so energy of your photons is inversely proportional to the wavelength do not say in directly use the word inversely if we plot a graph of the energy versus the wavelength will have an inverse proportionality graph but if we plot the graph of energy of the photons versus 1 over wavelength that is a direct proportionality so that will give us a straight line graph to back to the particle nature and the wave nature of the spectrum the lower the frequency of the photons the lower the energy of the photons they will behave more like waves so for example microwaves which are second from the right-hand side on the sketch that we have they are the second shortest of all our electromagnetic waves they have low frequency therefore long wavelengths they will have more wave nature than particle nature the invisible light it falls in the middle of the electromagnetic spectrum it therefore has dual nature it has wave nature and particle nature you might hear someone talk about the dual nature of light that is because light visible light has wave nature and particle nature when more growth that I would like to look at is the graph of frequency versus wavelength remember from our wave equation the speed of electromagnetic waves is equal to the product of the frequency and the wavelength of the waves the higher the frequency the lower the wavelength will the lower the frequency the longer the wavelength because these two values always have to multiply to give you the same constant three times ten to the eighth meters per second so frequency is therefore inversely proportional to wavelength and our graph would give the inverse proportionality if they asked you to draw a graph of frequency versus one over wavelength it would be a straight line graph through the origin the higher the frequency the shorter the wavelength because frequency and wavelength or inverse proportionality x' in grade 11 you did two chapters on wave nature you did a chapter on the refraction of light using Snell's law and you also did a chapter on 2d and 3d waves which involved diffraction and interference so diffraction interference and refraction are all proof of wave nature proof of particle nature is the photoelectric effect and that is what we are doing in grade 12 so you must know that Nishan of the photoelectric effect it is the process whereby electrons are ejected from a metal surface when light of suitable frequency is incident on that surface in order to eject electrons from a metal the frequency of the incident light must be greater than the threshold frequency of the metal each metal has its own particular threshold frequency so if your frequency of your incident light of the from the electromagnetic spectrum is greater than the threshold frequency of the metal electrons will be emitted or ejected from that piece of metal another word for threshold frequency is called the cut-off frequency the definition of threshold frequency or cutoff frequency it is the minimum frequency of light needed to emit electrons from a certain metal surface the symbol that we use is a small letter F with a subscript 0 please make your subscripts look like subscripts a lot of you are being penalized in your tests and exams because your subscripts are written too high or too big the definition for the work function which is the capital W for work with a subscript zero work function is the minimum energy that an electron in the metal needs to be emitted from the metal surface so to calculate work function it is Planck's constant times the threshold frequency for that particular metal threshold frequency and work function offset or they are fixed for each particular metal that does not change if the energy of the photons is greater than the work function of the metal electrons will be emitted with a certain kinetic energy EK the following equations are all extremely important but they are given to you on your data sheets this is the energy of the photon that is incident on the metal so there is your electromagnetic photon incident metal this rectangular thing here is our metal and these are our electrons inside the metal the work function w0 is the amount of energy needed to get the electron from within the middle to the surface and then if there is any energy remaining that will be the kinetic energy with which the electron moves away from our metal surface E is calculated by Planck's constant times the frequency of your incident light there it is w0 is your work function which is calculated by Planck's constant times the threshold frequency of the middle and EK is the normal equation for calculating kinetic energy half MV squared the mass of an electron is given to you on your daughter sheet please remember that you might get a question in the exam and they don't give you the mass of an electron you do actually have it it's on the data sheet a quick look at the sketch again this is the photon of light from your electromagnetic spectrum falling in on your metal he is equal to H if in red there we go the work function in green is the energy needed to get the electron to the surface and then the energy in blue is the kinetic energy of the electron as it moves away from the metal surface if your energy of your photon is equal to the work function your electron will just be able to go to the surface it will have no extra kinetic energy to move away from the surface of the metal the electrons that are removed from a metal and the influence of photons are called photo electrons there are normal electrons but they're called photo electrons we are now going to study the kinetic energy versus frequency graph for the emitted electrons for now just ignore the graph and look on the right-hand side if we consider the general equation for straight line graph you know it is y equals MX plus C or F of X equals MX plus C this is your vertical axis so in this case it's kinetic energy M is your gradient X is your horizontal axis in this case it is the frequency of the incident light and C is your y-intercept we are going to arrange our equation which was e equals W zero plus e K but in the place of E I'm putting in H F and we are going to manipulate this equation to fit the axes of the graph so I want EK to be on the left hand side where the Y is because it's my vertical axis and I want frequency to be in the place where X is because that is my horizontal axis so the equation becomes this EK equals hf minus the work function so I made EK the subject of the equation if you - work function on both sides it becomes H if - work function so that is what our equation looks like now it is the same form as the general equation for straight line graph y equals MX plus C Y is our e K our vertical axis H is M which is the gradient so you can see the gradient of this graph is Planck's constant the slope represents H Planck's constant X in this case is our frequency and C is our work function so the y-intercept of this graph is the work function you can see this is an energy energy and work are in joules this is our energy axis and that is our frequency axis the x intercept or the frequency intercept is the threshold frequency of our particular metal and once again the slope is the the gradient is Planck's constant so this is the graph for EK equals h if - work function there at the equation is w 0 work function of the metal is the intercept of the vertical axis and the gradient represents Planck's constant all of these graphs will have the same gradient irrespective of which metal we use and irrespective of which section we use from the electromagnetic spectrum as you can see from this graph any frequency lower than the threshold frequency will not give the electron any kinetic energy to leave the metal the frequency that is equal to the threshold frequency will not give the electron any kinetic energy but it will just get the electron to the surface of the metal if I choose a frequency slightly higher than the threshold frequency say for example a frequency over here you would take that frequency draw your dotted line up to your graph draw it across and then you could read off what the kinetic energy of that electron would be as it leaves the metal the higher the frequency of the incident light as long as it's above the threshold frequency higher frequency will give your electron a higher kinetic energy as it leaves the metal in this sketch we have a few graphs for different types of metals the same as the previous graph on the vertical axis we have the maximum kinetic energy of the electron which is leaving the metal on the horizontal axis we have the frequency of the incident light the threshold frequency is given for each particular metal as you can see each particular metal has its own threshold frequency so we'll look at potassium potassium first this is the threshold frequency potassium has the lowest threshold frequency there is its work function for sodium the work function will be lower down it will be weird intercepts with a vertical axis and it's threshold frequency is higher it has greater work function and greater threshold frequency if we go up to platinum of all these metals in them has the highest highest threshold frequency so it needs the most energy to get an electron to the surface I want you also to notice that all of these graphs have the same slope they have the same gradient because the gradient represents Planck's constant it will never change you will always have the same gradient you have the value for Planck's constant 6.6 3 times 10 to the negative 34 joules times second so if you were ever asked to calculate anything from a graph like this and you have certain values that you can read off remember you have the gradient of the graph the question above the graph is which metal requires the greatest or minimum energy to begin to eject electrons which metal requires the least energy to eject electrons potassium requires the least energy it's got the lowest threshold frequency and the lowest work function potassium requires the most energy to release electrons because it has the highest threshold frequency and it would have the highest work function the next question what does this mean with respect to how tightly electrons are bound to an atom in which one would you say are the electrons the most tightly bound in which one requires would require more energy to remove electrons from the atom Platinum would require the most energy from a photon to remove electrons from the surface of the metal because platinum has the highest threshold frequency and if we had to extrapolate this graph back down to the vertical axis it would also have the greatest work function so in platinum the electrons would be more tightly bound to the atom than in potassium potassium has the lowest threshold frequency it will have the lowest work function therefore it would lose electrons the easiest of all of these metals platinum would require the most energy to have electron removed you may get a question involving an electroscope an electroscope is just an apparatus that when it is positive or negatively charged the gold leaf will move away from the other piece of metal because they have the same charge so repulsion takes place in the first example you your electroscope can be positive or negatively charged but so that when red laser light is shone on it you know that red light has got a low frequency therefore low energy of the photons so whether this electroscope is positively or negatively charged it won't have any effect so there's no effect on the electroscope our next electroscope is positively charged that means that electrons have been removed so the positive goldleaf is repelled by the other plate which is normally zinc or platinum so the gold leaf is repelled by the other metal if of ultraviolet light is shown on the positively charged electroscope nothing happens because ultraviolet light has a very high frequency therefore high energy of the photons so it can remove electrons which would just make the electroscope more positively charged so in this case nothing happens there's also no effect because your electroscope is positively charged it has too few electrons so this very very little chance that you're ultraviolet light will remove more electrons in the third example our electroscope is negatively charged so something was done to give it a negative charge so the while it's negatively charged it would look like this the gold leaf would also be repelled by the other metal because they both would be negatively charged but when the ultraviolet light with high frequency therefore high energy is shown onto the plate electrons will be ejected or emitted from the electroscope so the plate will lose those extra electrons and the gold leaf will go down the difference between these two is ultraviolet light on a positively charged electroscope it has already lost electrons so it won't want to lose more so it no change takes place there in this one the electroscope is negatively charged so in the high frequency ultraviolet light high-energy photons shine onto the metal electrons will be removed so it will lose its negative charge and the plate the gold leaf will go down to the other metal plate in this sketch we will be looking at the photo cell which works under the influence of incident light photons fall onto the cathode electrons are emitted and they move towards the anode and flow through the external circuit an ammeter or micro milli ammeter is used to measure the current strength the cathode is connected to the negative terminal of the cells and the anode is connected to the positive terminal of the cells so your intensity of your life determines the current strength but just remember that the frequency of your incident light must be greater than the threshold frequency for electrons to be emitted an increase in the frequency of the incident light will increase the kinetic energy of the emitted electrons if we change this equation to what it is on the right hand side all I have done is replaced a with HF the greater the frequency of your incident light this is constant for the metal the greater the kinetic energy of the electrons moving away from the metal but if we change the intensity of the incident light in other words a brighter light if you increase the intensity of the incident light that means you have increased the number of photons falling in on the metal this will increase the number of electrons emitted from the metal and that will lead to an increase in the current strength measured by the emitter in the photocell so do not confuse these two and increase in frequency with an increase in in intensity of the

Channel: Science With Cecile

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Keywords: photoelectric effect, physics, particle nature of light, IEB, grade 11, grade 12, waves, frequency, wavelength, speed, electronmagnetic waves, spectrum, visible spectrum, gamma rays, X rays, infrared, radiowaves, microwaves, physical science, CAPS, syllabus

Id: fWwlnRbVq5w

Length: 21min 59sec (1319 seconds)

Published: Mon May 06 2019