Phoroelectric Effect Part 2

Added: 2026-05-11

[00:00:08]So in the last class we have seen about the photoelectric effect the phenomena of photoelectric effect and its theory and we have seen that uh the frequency of incident light should be greater or must be equal to the throld frequency that is the minimum frequency. of the metal to produce photo electrons.

[00:00:35]Now in this um class we will see the Einstein contributions towards the photoelectric effect.

[00:00:48]So the photoelectric effect is pro uh pro process that involves ejection or release of electrons from the surface of materials generally metals when light falls on them. The photoelectric effect is an important concept that enable us to clearly understand the quantum nature of the light and electrons.

[00:01:15]After continuous research in this field, the explanation of the photoelectric effect was successfully explained by Albert Einstein and he concluded that the effect occurred as a result of light energy being carried in the discrete quantized package not continuous but it is discrete.

[00:01:39]For this excellent work he was honored with Nobel Prize in 1921.

[00:01:47]So according to Einstein each photon of the energy E is given by E is equal to H new as we know that from the planks equation where E is the energy of the photon in the jewel as is the plank's constant whose value is 6.625 625 into 10 ^ -34 JW and new is the frequency of the photon in the hertz. So what are the properties of photon? For a photon its quantum number are zero. A photon does not have any mass or charge and they are not reflected and in the magnetic and electric field. The photons moves at the speed of light in the empty space.

[00:02:32]During the interaction of the matter radiation and uh radiation behave as it may make of the small particles called photons. Photons are virtual particles.

[00:02:46]The photons energy is directly proportional to the frequency and inversely proportional to the its wavelength. The momentum and the energy of the photons are related which is given by E is equal to PC.

[00:03:02]Okay. Is equal to PC as we know that uh the equation is E is equal to<unk> over M uh C² + P² + C² M C ^ 4. Um so if we put mass is equal to zero then we have E= PC. So here we have E is equal to PC.

[00:03:31]um m² c to the power 4 sorry m² c to the power 4 this is the relativistic equation of energy so here m for photon m is equal to zero so if we put m is equal to0 then e is equal to directly gives e is equal to pc and p is the magnitude of the momentum and c is the speed of the light the definition of the photoelectric effect the phenomena of metal releasing electron when they are exposed to the light of the appropriate frequency is called the photoelectric effect and the electrons emitted during the process are called photoelerons.

[00:04:14]The principle of photoelectric effect the law of conservation of energy from the basis of photoelectric effect.

[00:04:22]So we are seeing the definition of photoelectric effect. The phenomena of metal releasing the electrons when they exposed to the light of appropriate frequency is called the photoelectric effect. And the electrons emitting during the process are called photoelerons.

[00:04:40]The principle of photoelectric effect.

[00:04:42]The law of conservation of energy forms the basis of the photoelectric effect.

[00:04:46]We will see the u law of conservation energy.

[00:04:51]The minimum condition for the photoelectric effect which is the throl frequency. So it is the minimum frequency of the incident light or radiation that produce a photoelectric effect that is ejection of photoeleron from the metal surface is known as the throl frequency for the metals. It is constant for a specific metal but may be different for different metals. So if new is the frequency of um new is the frequency of incident photon and new th is the throl frequency. Then uh new if new the frequency of incident photon is less than the throl frequency there will be no ejection of photoeleron and there is no photoelectric effect. And if uh new is equal to throl frequency the photo electron was just ejected from the metal surface. In this case the kindinetic energy of the electron is zero.

[00:05:54]And the third case when the new is greater than throl frequency then the photo electron will come out from the surface along with the kinetic energy.

[00:06:04]So using this we will derive the phen uh derivation of the photo photoelectric equation. So next is throld wavelength. So during the emission of electrons a metal surface corresponding to the greatest wavelength to the incident light is known as the inc thold wavelength. So as we know that new th is a throld frequency. So lambda TH that is throld wavelength is equal to C divided by new TH. As we know that C is equal to new lambda. So using this equation uh we have lambda is equal to C by new. So new TH is equal to C by new TH. This is the equation of throl wavelength. So wavelength above this throl there will be no photo electron emission.

[00:07:08]And for lambda is equal to wavelength of incident photon. Then as we know uh that the lambda is inversely proportional to frequency. So uh we have three conditions that if new is uh the frequency of incident where light um is greater than the threshold frequency. So no photo electric photo no photoelectric effect.

[00:07:46]If new is nearly equal to new th there will be photoelectric effect. Photo electric effect but the kinetic energy is equal to in this case is equal to zero. And if new is greater than new th we we have photoelectric effect photoelectric effect with kinetic energy.

[00:08:18]So as we know that lambda is inversely proportional to new. So in this case we have another three result that is number one lambda uh is greater than uh in this case we will use uh previously.

[00:08:46]So if lambda that is the wavelength of the incident light is less than uh lambda th okay if lambda is less than here we have seen that if lambda is less than throld wavelength then the photoelectric effect will take place.

[00:09:08]Number two, if lambda is equal to lambda th that is the wavelength of throl frequency then just the photoelectric effect take place but the kindinetic energy is zero and number three if lambda is greater than lambda th so no photoelectric effect. So we have to remember these three condition and with these three condition we will derive these three condition.

[00:09:39]Okay.

[00:09:41]Now next is work function or throl energy.

[00:09:47]The minimum energy of thermodynamic work that is needed to remove an electron from the conductor to a point in the vacuum immediately outside the surface of the conductor is known as the work function or throld energy. So this thirst energy ph we denoted as phi is equal to as we know energies according to fun equation we have e is equal to h now so we have using um phi in place of e because phi is the throl energy so thole energy is equal to h and in place of new we have new th because it is associated with the throl now H and in place of new TH we can write it as C / lambda TH as we know that U C is equal to new lambda.

[00:10:49]So uh lambda uh new is equal to C by lambda and giving TH subscript here. So new th is equal to c by lambda th. So we are using this equation here. Here work function is characteristics of the given metal. If e is the energy of the incident photon then if e is less than five that is the throl energy no photoelectric effect will take place. If E is equal to five just a photoelectric effect but the kindinetic energy of ejected photoeleron will be zero. and E.

[00:11:34]If E is if E is greater than photo electrons will be zero and E if if E is greater than five the photo electronic effect will take place along with the position of the kinetic energy by the ejection of electrons. Now next is photoelectric effect formula with the help of Einstein's explanation. So Einstein's g photoelectric formula with the help of conservation of conservation of energy that is before energy that is before energy uh that is the uh before the photoeleron um takes case. So before energy and after uh electrons are removed from the metals both energy should be equal or the total energy of the system should be conserved.

[00:12:58]So the energy of the photon is equal to energy needed to remove an electron plus kindinetic energy of the metal. So we as we know that there if this is the metal this is the incident wavelength and after sometimes photo electrons are emitted photo electrons plus kinetic energy.

[00:13:27]So this is the energy photon we this is they are photon energy of photon uh this is the energy of photo electrons plus kinetic energy. So we can write it as energy of the photon is h new. Energy needed to remove an electron is denoted by W. And the kindinetic energy of the imitator is capital E where H is the planks constant, new is the frequency of the incident photon, W is the work function and E is the maximum energy kindinetic energy of the ejected electron which is given by half MD². So law governing the photoelectric effect for a light of given frequency new is greater than thol frequency.

[00:14:13]The photo electro electric current is directly proportional to the intensity of light.

[00:14:20]Intensity of light g intensity g photoelectric current.

[00:14:26]Next is for any given material there is a certain minimum energy called throl energy frequency below which the emission of photoeleron stops completely no matter how high the intensity of incident lights that that means new should be greater than new th or maybe some cases if we need no kinetic energy This equation should be satisfied for photoelectric effect to take place. Photo electric effect to take place.

[00:15:06]The maximum kindinetic energy of the photo electron is found to be increased with the increase in the frequency of the incident light provided that the new should be greater than new exceeds the threshold limit. The maximum kinetic energy is independent of the intensity of the light.

[00:15:25]The photo emission is an instantaneous process. That means as the photo as the photons are strikes on the metals at the same time photo electrons if this condition is satisfied photo electrons started uh comes out from the metal surface.

[00:15:50]Experimental study by photoelectric fed that is photoelectric fed. Uh this is an evacuated quas tube. There are two electrons. This is cathode.

[00:16:05]This is anode.

[00:16:09]And light is light or photons are emitted on the cathode tube.

[00:16:17]A voltmeter voltmeter is connected parall to the circuit.

[00:16:26]There is a resistance box, battery and ampmeter which measure the current produced during this process.

[00:16:37]So the given experiment is used to study the photoelectric effect experimentally.

[00:16:42]It is the evacuated gas tube of two plates C and D. Two jinx plates C and D.

[00:16:50]Our enclosed plate C act as a this is C C and this is D.

[00:16:58]C acts as a cathode.

[00:17:01]Sorry C act as a anode. We have C and D.

[00:17:04]Sorry sorry sorry.

[00:17:07]This is C and this is D.

[00:17:16]C acts as a U anode and D act as a photosensitive plate. Two plates are connected to a battery B and amter A. If the radiation incident on the plate D plate D this is plate D through a quartz window W electrons are ejected out of the plate and current flow in the circuit. This is known as photo current. Plate C can be maintains as a desired potential positive negative with the help of plate D. Okay.

[00:17:55]Now characteristics of the photoelectric effect. So number one characteristic is the the thrust frequency varies with the materials. It is different for different materials. That is uh new th is the value of new th is different for different materials.

[00:18:23]So the value of new will be as we know that new should be greater than new th. So if new th is different. So new this condition is new that is the value of new will be different for different material.

[00:18:42]The photoelectric current is directly proportional to the light intensity.

[00:18:47]Okay, they are this is equ two. Number three, the kindinetic energy of the photoelectric electrons is directly proportional to light frequency. And number four, the stopping potential is directly proportional to the frequency and it process is instantaneous.

[00:19:05]Now factor affecting the photoelectric effects. With the help of this apparatus, we can now study the dependence of the photoelectric effect on the following factors that is intensity of uh incident radiation. Number two, the potential difference between the metal and uh um plate and the collector and number three the frequency of incident radiation that is I, V and new. So number one uh this is number one that that is the intensity effect of intensity of incident radiation or the photoelectric effect.

[00:19:44]The potential difference between the metal plate collector and frequency of incident light is kept constant and intensity of light is v. In the first case, we will kept uh the potential difference between the metal plate collector and the frequency of incident light to be constant and we will vary the new the frequency the intensity of light should sorry we will intensity. So that is vary the intensity not new we will vary the intensity of the light.

[00:20:21]So electro C that is the collecting electrode is made positive with respect to D metal plate for a fixed value of frequency and the potential between the metal plate and collector of photoelectric current is noted in the accordance with the intensity of incident radiation. It shows that the photoelectric current and intensity of instant radiation both are proportional to each other. Photoelectric if uh uh photoelectric current and the intensity of incident radiation both are proportional to each other. The photoelectric current gives the account to number of photoeleron rejected per second. Next is number two.

[00:21:04]The effect of potential difference between the metal plate and the collector on the photoelectric effect.

[00:21:11]The frequency of incident light and the intensity is kept constant. In this case, the intensity light frequency of intens light and the intensity is kept constant and the potential difference that is V uh between the plates is varied. Keeping the intensity and frequency of light constant, the positive potential of C is increased gradually. Photoelectric current increases with there is an positive increase in the potential difference in the metal plate and the collector up to the characteristics value. There is no change in the photoelectric current when the potential is increased higher than than the characteristic value for a increase in the accelerating voltage.

[00:21:51]This maximum value of current is called saturation current. So uh we if we increase the value of the potential difference there will be a maximum value after which uh the value of photoelectric current will not increase. This maximum value of current that is photocurren is called the saturation value that is the maximum value of the current. Number three, the effect of frequency of the photoelectric effect in this case with the intensity of light is kept constant and the frequency of light that is new is varied for a fixed uh intensity of incident light. Variation in the frequency of incident light is produced in the linear variation the cutff potential stopping potential of the metal. It is shown that the cutff potential VC is nearly proportional to the frequency of incident light.

[00:22:55]The energy kinetic energy of the photo electron increases directly proportional to the frequency of incident light. To completely stop the photo electrons, we should re reverse the increase and increase the potential between the metals and the collector. So the emitted photo electrons can't be reached to the collector.

[00:23:15]Now next is the Einstein photoelectric equation. So according to Einstein theory of photoelectric effect when the photons collides inelastically with the electrons the photon is absorbed completely or partially by the electrons. So if the electrons is metal absorb the photonss of the energy it uses the energy in the following ways.

[00:23:38]Sum of the energy that is phi KN you use to making the surface electron free from the metal it is known as work function of the material. Rest energy will appears as the kinetic energy of the emitted photo electrons. So we are Einstein photoelectric equation explains the following concepts. The frequency of the incident light is directly proportional to the kinetic energy of the electrons and wavelength of the incident light in inversely proportional to the kinetic energy of the electrons.

[00:24:14]New if new is equal to new th or lambda sorry lambda is equal to lambda th that is the as we know the kindinetic energy is zero. So maximum vax is equal to zero.

[00:24:33]Uh if lambda sorry if new is less than mu is less than new th or lambda is greater than lambda t there is no emission of photoel electrons. The intensity of radiation of the incident light refers to the number of photons in the light beam. More intensity means more photons and vice versa. Intensity has nothing to do with the energy of the photons and therefore the intensity of radiation is increased and the rate of emission increases but there will be no change in the kindinetic energy of the electrons. With an increasing number of emitted electrons the value of photoelectric current increases.

[00:25:16]So we have uh se seen uh three factors affecting the uh this phenomena that is the intensity of incident radiation, potential difference and frequency. So we will plot some graph according to with this that is the different graphs of photoelectric equation. This is very important. So number one is the photoelectric current with versus uh potential of the different voltages. Number two is photoelectric current with the potential of different intensities.

[00:25:51]Electric current and light intensity stopping potential versus frequency.

[00:25:55]Electric current and light frequency and electron and light frequency. We will see it one by one. So number one is this is the graph of uh uh there number one graph is potent photoelectric current versus potential of different voltage.

[00:26:19]So if we this is y-axis and this is x-axis.

[00:26:26]In the x-axis we have anode potential.

[00:26:29]In the y-axis we have photoelectric current. So for different frequencies this is the maximum value of the current which is called as maximum value of current shown in the ammeter.

[00:26:51]So for different this is maximum. So it is called saturation current.

[00:26:58]Uh we have three frequency retardant potential. Uh number one, V_sub_1, V2 and V_sub3. So as the potential increases, this is the negative sign.

[00:27:11]The curve g slightly move towards the anode potential and it coincide or intersect or meeting at the point where we have the maximum potential maximum current.

[00:27:30]This is the photoelectric current effect with the help with the anode potential.

[00:27:36]Next is potential or collector potential with the photoelectric current. So this is saturation current maximum value. We have three um currents value that is I1, I2 and I3.

[00:27:58]Uh here I1 is greater than I2. I2 is greater than I3.

[00:28:04]So as we know that for different values of I1, I2, I3 but the stopping potential where the the value of the potential where photo electrons stops emitted from the metal surface is same for different values of photoelectric. IC current.

[00:28:37]The third one is the light intensity and photoelect. As we know that this light intensity and photo electron is directly proportional in all cases we know as the if a and b are directly proportional in the all cases we have a graph passing through the origin. So this is the this gives the directly proportionality condition.

[00:29:03]with the photo uh current electron current and light intensity. If a is the current and I is the intensity, so A is directly proportional to I.

[00:29:21]Now stopping potential. So frequency and stopping potential the max minimum value um of v node where photo electron stops this is the value which gives the work function.

[00:29:41]Next is the electric current and the light frequency. So it is the constant uh so there will be a straight line uh which is parall to the x-axis or light frequency.

[00:29:57]Uh the last one is the light frequency and the photoelectric current. This is also the values of certain where the work function is there. And then this straight line that is directly proportional light frequency is directly proportional to to the electric electron kinetic energy. Now there are some applications of photoelectric effect used to generate the electricity in the solar panels.

[00:30:25]These panels contains metal combinations of the allow electricity generation um from the wide range of wavelength.

[00:30:35]Uh motion of the positive sensors in this case the photoelectric material is placed in the front of UV and IR led when the object is placed in between the light emitting diode and sensor and light is cut off and the electron uh resistor and change in the potential difference. There are light sensor. It is also used in light sensor. This is not very much uh useful um in our quantum mechanics. Uh um but we are seeing some applications to know the photoelectric effect where it it is used in experimental physics.

[00:31:16]It is also used in X-ray photoelerons uh spectroscopy that is XPC.

[00:31:23]Okay. In or used in the video camera tubes in the early days of television, it is used in the photo multipliers to detect the low level of light.

[00:31:33]Uh photoelectric cells are used to burglar the so that's it. The we have completed the photoelectric effect uh Einstein theory and everything in this section. Now next uh will be our corner topic will be debuggy wavelength and the dual nature of light. We will see it in the uh next upcoming classes.

[00:32:09]So we are seeing the definition of photoelectric effect. The phenomena of metal releasing the electrons when they exposed to the light of appropriate frequency is called the photoelectric effect and the electrons emitting during the process are called photoelerons.

[00:32:27]The principle of photoelectric effect the law of conservation of energy forms the basis of the photoelectric effect.

[00:32:33]We will see the u law of conservation energy the minimum condition for the photoelectric effect which is the throlid frequency. So it is the minimum frequency of the incident light or radiation that produce a photoelectric effect that is ejection of photoeleron from the metal surface is known as the throl frequency for the metals. It is constant for a specific metal but may be different for different metals. So if new is the frequency of um new is the frequency of incident photon and new th is the throl frequency. Then uh new if new the frequency of incident photon is less than the throl frequency there will be no ejection of photoeleron and there is no photoelectric effect. And if uh new is equal to throl frequency the photo electron was just ejected from the metal surface. In this case the kindinetic energy of the electron is zero.

[00:33:41]And the third case when the new is greater than throl frequency then the photo electron will come out from the surface along with the kinetic energy.

[00:33:52]So using this uh we will derive the phen uh derivation of the photo photoelectric equation. So next is throld wavelength. So during the emission of electrons a metal surface corresponding to the greatest wavelength to the incident light is known as the inc thold wavelength. So as we know that new th is a throld frequency. So lambda th that is throl wavelength is equal to c / new th as we know that c is equal to new lambda. So using this equation uh we have lambda is equal to c by new. So new th is equal to c by new th this is the equation of throl wavelength. So wavelength above this thursold there will be no photoeleron emission.

[00:34:56]And for lambda is equal to wavelength of incident photon then as we know uh that the lambda is inversely proportional to frequency. So uh we have three conditions that if new is uh the frequency of incident where light um is greater than the threshold frequency. So no photo electric photo no photoelectric effect.

[00:35:33]If new is nearly equal to new th there will be photoelectric effect photo electric effect but the kinetic energy is equal to in this case equal to zero. And if new is greater than new th we we have photoelectric effect photoelectric effect with kinetic energy.

[00:36:06]So as we know that lambda is inversely proportional to new. So in this case we have another three result that is number one lambda uh is greater than uh in this case we will use uh previously.

[00:36:34]So if lambda that is the wavelength of the incident light is less than uh lambda th okay if lambda is less than here we have seen that if lambda is less than throld wavelength then the photoelectric effect will take place.

[00:36:55]Number two, if lambda is equal to lambda th that is the of wavelength of throl frequency then just the photoelectric effect take place but the kindinetic energy is zero and number three if lambda is greater than lambda th so no photoelectric effect. So we have to remember these three condition and with these three condition we will derive these three condition.

[00:37:26]Okay.

[00:37:28]Now next is work function or throl energy.

[00:37:35]The minimum energy of thermodynamic work that is needed to remove an electron from the conductor to a point in the vacuum immediately outside the surface of the conductor is known as the work function or throld energy. So this throl energy phi we denote it as phi is equal to as we know energies according to fun's equation we have e is equal to h no so we have using um phi in place of e because phi is the throld energy so thole energy is equal to h and in place of new we have new th because it is associated with the thol Now h and in place of new th we can write it as c divided by lambda th as we know that u c is equal to new lambda.

[00:38:36]So uh lambda uh new is equal to c by lambda and giving th subscript here. So new TH is equal to C by lambda TH. So we are using this equation here. Here work function is characteristics of the given metal. If E is the energy of the incident photon then if E is less than five that is the throld energy no photoelectric effect will take place. If E is equal to five just a photoelectric effect but the kindinetic energy of ejected photoeleron will be zero. and E.

[00:39:22]If E is if E is greater than photo electrons will be zero and E if E is greater than five the photoeleronetic effect will take place along with the possession of the kindinetic energy by the ejection of electrons. Now next is photoelectric effect formula with the help of Einstein's explanation.

[00:39:58]So Einstein's g photoelectric formula with the help of conservation of conservation of energy that is before energy that is before energy uh that is the uh before the photoeleron u takes case. So before energy and after uh electrons are removed from the metals both energy should be equal or the total energy of the system should be conserved.

[00:40:45]So the energy of the photon is equal to energy needed to remove an electron plus kinetic energy of the metals. We as we know that there if this is the metal this is the incident wavelength and after sometimes photo electrons are emitted photo electrons plus kinetic energy.

[00:41:14]So this is the energy photon we this is they are photon energy of photon uh this is the energy of photo electrons plus kinetic energy. So we can write it as energy of the photon is h new. Energy needed to remove an electron is denoted by W. And the kindinetic energy of the imitator is capital E. Where H is the planks constant.

[00:41:40]New is the frequency of the incident photon. W is the work function and E is the maximum energy kindinetic energy of the ejected electron which is given by half MD². So law governing the photoelectric effect for a light of given frequency new is greater than throl frequency the photo electro electric current is directly proportional to the intensity of light intrinsity of light greater intensity greater photoelectric current.

[00:42:14]Next is for any given material there is a certain minimum energy called thol energy frequency below which the emission of photoeleron stops completely no matter how high the intensity of incident lights that that means new should be greater than new th or maybe some cases if we need no kinetic energy This equation should be satisfied for photoelectric effect to take place. Photo electric effect to take place.

[00:42:54]The maximum kindinetic energy of the photoeleron is found to be increased with the increase in the frequency of the incident light provided that the new should be greater than new exceeds the threshold limit. The maximum kinetic energy is independent of the intensity of the light.

[00:43:13]The photo emission is an instantaneous process. That means as the photo as the photons are strikes on the metals at the same time photo electrons if this condition is satisfied photo electrons started uh comes out from the metal surface.

[00:43:37]Experimental study by photoelectric effect that is photoelectric effect. Uh this is an evacuated quas tube. There are two electrons. This is cathode.

[00:43:52]This is anode.

[00:43:56]And light is light or photons are emitted on the cathode tube.

[00:44:04]A voltmeter.

[00:44:09]voltmeter is connected parall to the circuit.

[00:44:13]There is a resistance box, battery and ammeter which measure the current produced during this process.

[00:44:25]So the given experiment is used to study the photoelectric effect experimentally.

[00:44:29]It is the evocquated gas tube of two zinc plates C and D. Two jinx plates C and D are enclosed plate C act as a this is C C and this is D.

[00:44:46]C acts as a cathode sorry C act as a anode. We have C and D.

[00:44:51]Sorry sorry sorry.

[00:44:54]This is C and this is D.

[00:45:04]C acts as a U anode and D acts as a photosensitive plate. Two plates are connected to a battery B and amter A. If the radiation incident on the plate D plate D this is plate D through a quartz window W electrons are ejected out of the plate and current flow in the circuit. This is known as photo current. Plate C can be maintained as a desired potential positive negative with the help of plate D. Okay.

[00:45:42]Now characteristics of the photoelectric effect. So number one characteristic is the the thrust frequency varies with the materials. It is different for different materials. that is uh new th is the value of new th is different for different materials.

[00:46:11]So the value of new will be as we know that new should be greater than new th. So if new TH is different so new this condition is new that is the value of new will be different for different material the photoelectric current is directly proportional to the light intensity.

[00:46:34]Okay, they are this is equ two. Number three, the kindinetic energy of the photoelectric electrons is directly proportional to light frequency. And number four, the stopping potential is directly proportional to the frequency and it process is instantaneous.

[00:46:52]Now factor affecting the photoelectric effects. With the help of this apparatus, we can now study the dependence of the photoelectric effect on the following factors that is intensity of uh incident radiation. Number two, the potential difference between the metal and uh um plate and the collector and number three the frequency of incident radiation that is I, V and new. So number one uh this is number one that that is the intensity effect of intensity of incident radiation or the photoelectric effect.

[00:47:31]The potential difference between the metal plate collector and frequency of incident light is kept constant and intensity of light is v. In the first case, we will kept uh the potential difference between the metal plate collector and the frequency of incident light to be constant and we will vary the new the frequency the intensity of light. So sorry we will intensity. So that is vary the intensity not new we will vary the intensity of the light.

[00:48:08]So electrode C that is the collecting electrode is made positive with respect to D metal plate for a fixed value of frequency and the potential between the metal plate and collector of photoelectric current is noted in the accordance with the intensity of incident radiation. It shows that the photoelectric current and intensity of incident radiation both are proportional to each other. photoelectric if uh uh photoelectric current and the intensity of incident radiation both are proportional to each other. The photoelectric current gives the account to number of photoeleron rejected per second. Next is number two the effect of potential difference between the metal plate and the collector on the photoelectric effect.

[00:48:59]The frequency of incident light and the intensity is kept constant. In this case, the intensity light, frequency of incident light and the intensity is kept constant and the potential difference that is V uh between the plates is varied. Keeping the intensity and frequency of light constant, the positive potential of C is increased gradually. Photoelectric current increases with there is an positive increase in the potential difference in the metal plate and the collector up to the characteristics value. There is no change in the photoelectric current when the potential is increased higher than than the characteristic value for a increase in the accelerating voltage.

[00:49:38]This maximum value of current is called saturation current. So uh we if we increase the value of the potential difference there will be a maximum value after which uh the value of photoelectric current will not increase. This maximum value of current that is photocurren is called the saturation value that is the maximum value of the current.

[00:50:09]Number three, the effect of frequency of the photoelectric effect in this case with the intensity of light is kept constant and the frequency of light that is new is varied.

[00:50:22]For a fixed uh intensity of incident light variation in the frequency of incident light is produced in the linear variation the cutff potential stopping potential of the metal. It is so that the cutff potential VC is nearly proportional to the frequency of incident light.

[00:50:42]The energy kindinetic energy of the photo electron increases directly proportional to the frequency of incident light. To completely stop the photo electrons, we should reverse the increase and increase the potential between the metals and the collector. So the emitted photo electrons can't be reached to the collector.

[00:51:03]Now next is the Einstein photoelectric equation. So according to Einstein theory of photoelectric effect when the photons collides inelastically with the electrons the photon is absorbed completely or partially by the electrons. So if the electrons is metal absorb the photons of the energy it uses the energy in the following ways. Sum of the energy that is phi KN you use to making the surface electron free from the metal it is known as work function of the material. Rest energy will appears as the kinetic energy of the emitted photo electrons. So we are Einstein photoelectric equation explains the following concepts. The frequency of the incident light is directly proportional to the kinetic energy of the electrons and wavelength of the incident light in inversely proportional to the kinetic energy of the electrons.

[00:52:01]New if new is equal to new th or lambda uh sorry lambda is equal to lambda th that is the kind as we know the kindinetic energy is zero. So maximum vax is equal to has zero.

[00:52:20]Uh if lambda sorry if new is less than new is less than new th or lambda is greater than lambda t there is no emission of photo electrons. The intensity of radiation of the incident light refers to the number of photons in the light beam. More intensity means more photons and vice versa. Intensity has nothing to do with the energy of the photons and therefore the intensity of radiation is increased and the rate of emission increases but there will be no change in the kindinetic energy of the electrons. With an increasing number of emitted electrons the value of photoelectric current increases.

[00:53:03]So we have se uh seen uh three factors affecting the of this phenomena that is the intensity of incident radiation, potential difference and frequency. So we will plot some graph according to with this that is the different graphs of photoelectric equation. This is very important. So number one is the photoelectric current with versus uh potential of the different voltages. Number two is photoelectric current with the potential of different intensities.

[00:53:38]Electric current and light intensity stopping potential versus frequency.

[00:53:42]Electric current and light frequency and electron and light frequency. We will see it one by one. So number one is this is the graph of uh there number one graph is potent photoelectric current versus potential of different voltage.

[00:54:06]So if we this is y-axis and this is x-axis.

[00:54:13]In the x-axis we have anode potential.

[00:54:16]In the y-axis we have photoelectric current. So for different frequencies this is the maximum value of the current which is called as maximum value of current shown in the ammeter.

[00:54:38]So for different this is maximum. So it is called saturation current.

[00:54:45]Uh we have three frequency retardant potential. Uh number one, V_sub_1, V2 and V3. So as the potential increases, this is the negative sign. The curve g slightly move towards the anode potential and it coincide or intersect or meeting at the point where we have the maximum potential maximum current.

[00:55:18]This is the photoelectric current effect with the help with the anode potential.

[00:55:24]Next is potential or collector potential with the photoelectric current. So this is saturation current maximum value. We have three um currents value that is I1, I2 and I3.

[00:55:45]Uh here I1 is greater than I2. I2 is greater than I3.

[00:55:52]So as we know that for different values of I1, I2, I3 but the stopping potential where the the value of the potential where photo electrons stops emitted from the metal surface is same for different values of photoelectric. IC current.

[00:56:24]The third one is the light intensity and photoelect. As we know that this light intensity and photoelect is directly proportional.

[00:56:33]In all cases we know as the if a and b are directly proportional in the all cases we have a graph passing through the origin. So this is the this gives the directly proportionality condition.

[00:56:50]with the photo uh current electron current and light intensity. If a is the current and I is the intensity so a is directly proportional to I.

[00:57:08]Now stopping potential. So frequency and stopping potential. The max minimum value um of V where photo electrons stops.

[00:57:20]This is the value which gives the work function.

[00:57:28]Next is the electric current and the light frequency. So this is the constant.

[00:57:35]Uh so there will be a straight line uh which is parall to the x-axis or light frequency.

[00:57:45]Uh the last one is the light frequency and the photoelectric current. This is also the values of certain where the work function is there and then this straight line that is directly proportional light frequency is directly proportional to to the electric electron kindic energy. Now there are some applications of photoelectric effect used to generate the electricity in the solar panels.

[00:58:12]These panels contains metal combinations of the allow uh electricity generation um from the wide range of wavelength.

[00:58:23]uh motion of the positive sensors. In this case, the photoelectric material is placed in the front of UV and IR LED when the object is placed in between the light emitting diode and sensor and light is cut off and the electron uh resistor and change in the potential difference. There are light sensor. It is also used in light sensor. This is not very much uh useful um in our quantum mechanics. uh um um but we are seeing some applications to know the photoelectric effect where it it is used in experimental physics. It is also used in X-ray photoel electrons uh spectroscopy that is XPC.

[00:59:10]Okay. In or used in the video camera tubes in the early days of television.

[00:59:15]It is used in the photo multipliers to detect the low level of light.

[00:59:21]Uh photoelectric cells are used to burglar the alarm. So this that's it. The we have completed the photoelectric effect.

[00:59:32]uh Einstein theory and everything in this section. Now next uh will be our corner topic will be debug wavelength and the dual nature of light. We will see it in the uh next upcoming