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[00:00:00]Let's finish the modern physics in next 15 to 20 minutes. My dear nepants, I'm not going to leave any of the topics out there. Trust me, this is going to be very helpful. And if you want to leave any of the chapters out there, but do not leave modern physics. Okay. So, let's dive into the complete modern physics in next 15 to 20 minutes. First topic that we need to understand over here that is energy of a photon. We say energy of a photon is H into F. H means plank's constant, F means frequency. F we further say C divided by lambda. C is speed of light. Lambda is wavelength.

[00:00:24]So, we can say energy is equal to HC divided by lambda. So, value of planks constant is 6.6 6 into 10^ - 34 value of C is 3 into 10^ 8 and if you put the values of H and C over here you will finally get energy of photon 2 into 10^ -25 that is divided by lambda this lambda is in meters energy is in jewles okay then further my dear neat aspirants we further say energy of a photon is also equal to this that is 1240 and divided by lambda but here we take lambda instron and energy in electron volt and we also say energy of a photon is 1240 in electron volt but lambda is in nanometers so use this when you when lambda is given inron use this when lambda is given in nanometers likeminded aspirants If I say photon has got an wavelength of 4,000 in this particular case, we'll be using this to find the energy. If energy of a photon is then sorry if wavelength is in nanometer, we'll be using this to find the energy of a photon in this particular case.

[00:01:09]Let's dive into the next one. Now when it comes to the energy of light aspirin, energy of light is simply that means nf energy of light means energy of n number of photons large number of photons. So you can further write it nc divided by lambda because f is also c divided by lambda. Then my dear neat aspirants momentum of a photon. We say momentum of a photon is h divided by lambda where h is plank's constant and lambda is the boy's wavelength. Okay, this is also one more relation that I want you guys to remember. This is the relation between energy and momentum of a photon. E is equal to p into c. Okay, this relation also I want you to remember. This is what we call the moving mass of a photon because we say rest mass of a photon is zero. H divided by lambda c. Then my dear me as friends we define power of light. Power of light is simply energy divided by time. How much energy is falling? Like this bulb is sending more energy more photons every second. So power of this is large as compared to this. So power is energy upon time.

[00:01:54]Energy we write NHF divided by T. You can also write NHC divided by lambda into T. So from here you can also calculate number of photons per second also. Then my dear neaspirit intensity of light. Intensity is simply defined as defined as energy upon time into area.

[00:02:06]So we can also say power divided by area. This is the formula NHF divided by A into C. This is what we call the intensity of light. Then my dear neat aspirants we say in case of a point source if you have a point source we say intensity at r distance will be power divided by 4 pi r². Okay. In case of a line source means a tube light intensity at r distance will be power divided by 2 pi r into l. Then my dear neat aspirants we say radiation pressure. If light or radiation falls on the surface it creates pressure on the surface. And if it is completely absorbing surface we say pressure is I divided by c. Okay you can also write this force acting on the surface is I into a divided by c where i is intensity a is area and c is speed of light. If it is a completely reflecting surface in that case we say this pressure is 2 i divided by c and force will be 2 i a divided by c where i is intensity c is speed of light. This is for completely reflecting surface. Now my dear neat aspirants we have photoelectric effect. Photoelectric effect is when photons fall on the metal surface, light fall on the metal surface, electrons are ejected from the metal surface. This phenomena is called photoelectric effect. Okay. And then my dear neat aspirins we say uh uh experimental setup of photoelectric effect. When electrons fall on the metal surface, electrons are ejected from the metal surface. So my dear neat aspirins, we say uh when photon falls on the metal surface, the energy of a photon is used in work function. Work function is the minimum amount of energy required to pull the electrons from the metal surface. So basically when photon falls on the metal surface it gives the energy to the electron and that electron uses that energy in order to come out of the metal surface and and so that it moves further forward. So we say work function plus kindinetic energy maximum. This is what we call Einstein's photoelectric equation. And my dear neath aspirants we also say kinetic energy of electron is e kn where v is the stopping potential.

[00:03:34]You guys need to remember this also. And my dear neat aspirants when electrons photonss fall on the metal surface on this cathode electrons come out of this cathode and they start moving. When they start moving they create photocurren.

[00:03:43]And then my dear neat as principally make the graph between photocurren and emf. So it is something like this. It is something like this. And this potential where photocurren is zero. This is what we call the stopping potential. And at stopping potential kindinetic energy of the electron is EV kn. I can say it's something like this. Then my dear neat aspirants one more important thing. We say frequency is directly proportional to photon energy. Photon energy is directly proportional to energetic energy of electron which is directly proportional to the stopping potential.

[00:04:04]Similarly intensity is directly proportional to the number of photons which is directly proportional to the number of electrons which is directly proportional to the photcurren. Then my dear neat aspirants one thing I want you to remember over here stopping potential has a relation with frequency photocurren has a relation with intensity. If you take a look at these three graphs over here they have got same current. This is photocurren. Okay same photocurren. If photocurren is same means intensity of the three graphs is same. And if stopping potential is different so means frequency of the three is different because frequency has the relation with stopping potential.

[00:04:28]Here in this case we say stopping potential of two graphs is same. So frequency is same. And in this case we say photocurren is different. So midnight aspirin intensity is different.

[00:04:35]So intensity of this is greater than intensity of this. Then these are the different versions of Einstein's photoelectric equation. You can write it like this also. PH plus kindic energy maximum. Pi energy of photon is H into F. This you can write H into F where F not is threshold frequency minimum frequency required to pull the electron from the metal surface. EV V not. You can write it like this. You can write F is equal to C divided by lambda also. HC divided by lambda is equal to HC by lambda KN. This is threshold wavelength plus EV. You can write it like this also. Energy of photon is H into F and work function is H into F plus 1x2 MV square. And my dear need transference H.

[00:05:03]You can write it like this also. HC by lambda is equal to HC by lambda plus 1x2 MV square. Then my dear neat aspirants droy is wavelength matter wavelength.

[00:05:09]Droy said everything in this universe is a particle as well as it is a wave. Like this pen it is a particle as well as this is wave. And what is the wavelength of this? This particle you can say h divided by mv or h divided by p where mv is the momentum my dear aspirants. Now we say dro wavelength in terms of kinetic energy. Dro's wavelength in terms of kinetic energy over here. Okay.

[00:05:26]So we say in terms of kinetic energy this is drogenth in terms of momentum in terms of kindinetic energy which is h upon under root of 2 mk. Then dro's wavelength for a charged particle accelerated under potential difference delta v. So that is lambda is equal h upon under root of 2 mq delta v. h is blank constant m is mass q is charge delta v is the potential difference.

[00:05:41]Then my dear neat aspirin we said dro wthgenth for a relativistic particle relativistic particle is that particle which is having the speed approximately speed of light like electron proton which moves with a very faster speed.

[00:05:50]Okay it's dro wave length is this much.

[00:05:51]Okay. H 1 minus v square by c square. V is the speed of that particle. C is the speed of light. M not is the rest mass of that particle. V is the speed of that particle and h is blank's constant. Droy wavelength for a charged particle at rest placed in electric field. So it has wavelength. H divided by q. Q is charged P is electric field D is time. Then my dear neat aspirants if Dro is wavelength for a charged particle placed in the magnetic field if a charged particle is placed in magnetic field it is wave length with H upon QBR Q is charge B's magnetic field R is the radius because here rad particle moves in a circular path when it goes into the magnetic field perpendicularly for a gaseous molecule which is H upon under root of 3 M KBT where KB is the bolts man's constant and T is temperature for an electron moving in the nth orbit of an electron so we say it its debren is N into H upon under root of 2M into 13.6 physics then my dear neat aspirin we have atom we are done with the dual nature of matter and radiations now we have atomic physics first model of atom was thson's atomic model thson said that an atom is exactly like watermelon in which this this red portion which we eat it it it means positive charge and the seeds okay these seeds represent electrons okay seeds represent electrons and he also said atom is electrically neutral means number of positive charge the amount of positive charge in an atom is equal to the amount of negative charge okay so this was basically Thompson's model then my dear neat aspirants came the ratherford's atomic model ratherford's atomic model he performed an experiment that is what we call alpha particle scattering experiment and in that alpha particle sketching experiment he took alpha source from which alpha particles were coming out and it were crossing the gold foil and he observed 99.86% 86% alpha particles were directly crossing on the screen, directly crossing the gold foil and were falling on the screen and only 0.14% were deviating. That means 1 in 8,000 alpha particles are deviated. What does it mean? What does it mean? It means if all the alpha particles are alpha particle means positive charge if all the alpha particles are crossing. So means positive charge is not present in the entire sphere. If the positive charge is present in the entire circle then it would have repelled these alpha particles. Okay. So they said he said positive charge is present at a unique place that is what we call the nucleus.

[00:07:38]That is what we call nucleus. that electrons are revolving around the nucleus in in in random orbits not in a fixed orbit. So this was rather force atomic model. Then we said distance of closest approach. My dear me aspirants this is an alpha particle which is having the positive charge 2 E. If you throw this with an velocity V alpha so here you place an atom which is having the atomic number Z E. This is the charge on atom. All right people now my dear neat aspirants when you throw this when you throw this so this positive charged atom or positive charge nucleus it is going to repel this positive charge. So it will come close close at certain distance it will face maximum repulsion and it will be repelled back.

[00:08:09]This distance is what we call the distance of closest approach. And this distance of closest approach in terms of kindinetic energy is K Q1 Q2. Okay. So Q1 Q2 divided by kinetic energy. And our minimum in terms of atomic number you can write it over here E square upon pi epsylon mass of alpha particle into velocity of alpha particle square. This is distance of closest approach. Then my dear neasper bhor's atomic model bhar's first post says that an electron which is revolving in an orbit means means it is accelerating in an orbit. So whenever electron accelerates in an orbit it produces wave. He said it produces the stationary wave and stationary wave does not radiate the energy. It does not lose the energy. Hence an electron revolving in the uh in in in around the nucleus does not lose energy. So if it does not lose energy so electron will not collapse into the nucleus. Hence we say atom is stable. He define the stability of an atom. Then my dear nepirants bh second second postulate according to the second postulate my nepirants we say an electron revolves around only in those orbits where its angular momentum is n by dupi. So b second postulate says electron can only revolve in those orbits where its angular momentum is 2 pi. Not like Rutherford. Rutherford said here it revolves in the random orbits.

[00:09:08]Okay. N can be one. If n is one the angular moment will be h by 2 pi. If n is three it will be 3 h by I would say if n is two it will be n h by uh that is 2 h by 2 pi. Okay. Then while we need aspirins b's third postulate. B's third posture says that if electron revolves in the higher orbit and makes the transition to the lower orbit energy is released in the form of photon. If electron is revolving in the lower orbit makes the transition to the higher orbit. We say energy is absorbed in that particular case. Then mathematical analysis velocity of an electron in the nth orbit. This if if an electron is revolving in the nth orbit this is the nucleus having charge z its velocity will be e² epsylon h is blank constant z by n zed is the atomic number and my dear aspirants you can write it like this also 2.2 2 into 10^ 6 by N or V is Z by N. Okay, these are the two graphs.

[00:09:47]Okay, V versus N, V versus Z. Then radius of an electron in the nth orbit my dear dear dear dear dear dear dear dear dear dear nasperants. So we say if this is z and this is the radius r this electron is revolving in the n orbit. So this will be the radius r n² by z. This is the value of r or r not is 0.53 non also okay these are the three graphs which I would like you to understand over here between you can see it from your end only. Then the time period of an electron how much time an electron takes in completing one cycle that is t nqide square value of t not is this.

[00:10:12]Then my dear meat aspirins we say and n in this particular case means which orbit? Nth orbit if I'm talking about second orbit means n is 2. Frequency of an electron in the nth orbit. So frequency of an electron in the nth orbit is 2x3 10^ 16 square by nq. But magnetic field when an electron revolves around the nucleus it produce magnetic field at the center. How much magnetic field at the center? Bq by n^ 5. This is the value of b. Then min asparence total energy of an electron in the nth orbit.

[00:10:35]If an electron revolves in the nth orbit okay its kindinetic energy will be because it has mass it has velocity. It kindinetic energy will be Z E square 8 pi by epsylon R. Its potential energy will be minus Z E square upon 4 by pi epsylon R. So total energy will be total energy is kindinetic energy plus potential energy. So if you add these two it will come out to be minus Z E square upon 8 by pi epsylon R. Okay. You can also write total energy is negative of kindinetic energy. See total energy and kindinetic energy is exactly equal but this is negative. Or total energy is mod of mod of this is mod of this.

[00:11:00]Kindic energy is 1/2 of this much that is kinetic energy is potential energy divided by two. You can remember these EXPRESSIONS ALSO. OKAY. GRAPH BETWEEN ENERGY versus R. So kindinetic energy since positive. So graph will be from upper side. Total energy is negative and potential energy is negative. Graph will be from lower side. This is potential and this is total. Then my dear neat aspirants if we talk about hydrogen atom this is this is one more equation for total energy of an electron. So we say total energy of an electron is also equal to okay minus 13.6 okay z² divided by n square. For hydrogen atom we say zed is equal to my dear friends 1. So the 13.6 divided by n². So this is the energy of an electron in the first orbit in hydrogen atom - 13.6. In second orbit - 3.4 4 in third orbit - 1.51 you can see it exactly over here then my dear neat aspirin spectra when a white light is passed through the prism it is splitted into seven different colors vibr and then if you place a screen over here photographic plate over here and on the screen we say these different spots will be created red blue a violet indigo this creation of these spots is what we call the spectrum on the screen okay this creation of spots of different wavelength is called a spectrum now my dear neat aspirants you have absorption spectrum when an electron listen to me very carefully is revolving in this orbit and energy is 13.6 in the second orbit - 3.4 4. So this gap is 10.2 electron volts. If you subtract this from this, this is 10.2. If you send a photon of 10.2 electron volts, it is going to absorb that and make the transition to the higher orbit. When it makes the transition to the higher orbit on the screen, a dark spot is created.

[00:12:18]So on the bright screen, dark spot is created. This is called absorption spectrum because absorption spectrum means electron photon has been eaten up by the electron. That's why dark spot was created. And when an electron makes the transition from higher orbit to lower orbit, photon is released and which falls onto the spectrum on the screen. So prime spot is created. This is called emission spectrum. Okay. Then my dear neat aspirins this spectrum creation when electron moves from higher orbit to lower orbit this we show in the spectral series also in spectral series first is Lman series we show it then electron makes the transition from higher orbit to the first orbit okay like from second to first from third to first fourth to fifth first okay fifth to first okay so this we show in the LM series. So in Lyman series we show if electron moves finally to first orbit initially from second third fourth.

[00:12:56]Okay. So for first line energy is minimum frequency is minimum lambda is maximum. For last line energy is maximum we say frequency is maximum this is minimum. And similarly in bomber series we show if electron moves from higher orbit to the second orbit. Okay like this your final orbit in this case is two initial can be 3 4 5 and so on. And in partial series we say electron finally moves to the third orbit. Okay final is third. And in bracket series finally electron moves to the fourth orbit. Okay. And in P1 series finally electron moves to the fifth orbit. Now if somebody says this line how much wavelength this line actually has has this is the wavelength of the line when electron moves from higher orbit to lower 1x lambda r 1x n final square minus 1 by n initial square r is what we call the red word constant n final is the final orbit in which it is landing and initial is the initial orbit in which it is landing. Okay. Now if an electron makes the transition from higher orbit to the lower orbit like from third to first it can directly come from third to first it can come from third to second from second to first.

[00:13:42]How many lines are created? Three. How many spectral lines are created? This is the formula. N2 - n1 into n2 - n1 + 1 divided by 2. This is how we can find the number of spectral lines formed.

[00:13:50]Okay. Then my dear neat aspirants we have nuclei. When it comes to the chapter nuclei. So nuclei means nucleus means which is at the center of the atom. So inside the nucleus you have protons plus neutrons. These are what we call the nucleons. The particles which lie inside the nucleus are called nucleons. And representation of a nucleus is something like this. We say this is a letter and this is a this is z. A means mass number. Number of protons plus number of neutrons. Zed means atomic number of protons. A minus z means number of neutrons. Like this has mass number 10 atomic number five.

[00:14:15]So number of neutrons is also five in this case. Okay. rest mass energy if there is a mass okay due to the mass of an object energy is associated with it that is what we call rest mass energy and rest mass energy we say E is equal to MC² if let's suppose mass is 10 C is speed of light so energy in 10 kg is 9 into 10^ 17 Jew this is what we call the rest mass energy and size of nucleus or we say nuclear size so when we talk about the nuclear size that means the radius of nucleus we can write it like this radius of nucleus is r a ra^ 1x3 a means the mass number mass number r is basically the constant over here or we say volume of nucleus is v into a okay nuclear density of density of nucleus We say density of nucleus is simply 10^ 17 kg per meter cube. It is same for all the nuclei. Okay, it is same for all the nuclei. It does not depend upon the mass number. Then we say binding energy and mass effect. My dear neat aspirin if this is a nucleus. Okay. If it has mass number a atomic number z a minus z is the number of neutrons. Let's suppose it mass is m. If you break this nucleus in this particular case okay so means you use some energy in breaking the nucleus and you took all the nucle all the these protons out. How many protons? Z means number of protons. So zed mass of proton is MP. Z MP is the number of protons and this is the mass of Z protons and A minus Z is the neutrons. So mass of neutron is m and a minus z is the mass OF NEUTRONS. NOW WE saw that this mass came out to be greater than the collective mass. When they were inside they were having less mass. When they were outside they were having more mass.

[00:15:25]So we say mass defect has occurred. How to find that mass defect? Mass defect means this mass final mass mt plus a minus mn minus initial mass. And this mass defect is because when you break broke the nucleus the energy which is used in breaking the nucleus is stored in the form of mass of the nucleons.

[00:15:38]That's why mass defect occurred. So this energy which is used to break the nucleus is what we call the binding energy. Due to this binding energy only mass defect occurs. So binding energy is delta m into c square and this is the mass defect into I would say c square.

[00:15:48]You can see it over here. Then my dear aspirants we say binding energy per nucleon it is proportional to stability.

[00:15:53]Okay binding energy per nucleon means the amount of binding energy used so that you can take out one nucleon from the nucleus. So that is what we call the binding energy per nucleon. Okay. Graph between binding energy or stability versus mass number. See this is a graph.

[00:16:04]Now here we say mass number is 30. Here we say mass number is 70. Those nuclei which has got mass number less than 30.

[00:16:10]Those are what we call unstable nuclei.

[00:16:11]Those nuclei with mass number less than okay mass number less than mass number less than 30 those are called unstable nuclei. Now this end this is unstable.

[00:16:18]So they will basically fuse together. So between the nucle a is equal 30 to 170 these are stable nuclei. They will fuse together to form a bigger nuclei. Okay.

[00:16:25]So like 15 + 16 this is 31 mass number.

[00:16:27]So this is stable. So this process in which uh two nuclei fuse together to reach stability. This is what we call fision sorry fusion. So when a bigger nuclei breaks into smaller nuclei to attain stability this is called fision because see all of these have less binding energy for nucleon stability.

[00:16:40]This also has less. So this portion has got higher stability. That's why fish and fusion takes place. Okay. Yes. Q value of the reaction. We say when my dear neat aspirants a reactant nuclei are converted into product nuclei. In that particular case some energy is released or absorbed. This energy is what we call this energy released or absorbed is what we call the Q value of the reaction. And my dear neat aspirants when you talk about the Q value of the reaction listen to me very carefully.

[00:17:00]You said it is this Q value of the reaction will be mass of reactants minus mass of products into C square. So you can write it like this. This is reactants product minus mass of products into C square. A in terms of binding energy we write it like this. binding energy of products minus binding energy of reactants. So binding energy of C plus binding energy of D minus binding energy of A plus binding energy of B. So this will be Q value of the reaction.

[00:17:17]Okay. Yes. Now alpha beta plus DK beta minus DK alpha DK. We make a graph between number of protons plus number of neutrons. This curve is what we call stability curve. This nuclei this nuclei has got large number of neutrons. It is also unstable. This has got large number of protons. It is also unstable. This has got both large protons large neutrons. This is also unstable. So basically this nucleus will try to reach the stability curve. It will lose one neutron. It will gain one proton. Okay.

[00:17:38]Then again one neutron gains one proton it reaches stability curve. This process losing one neutron or converting one neutron into one pro proton this is called a beta minus dk aspirants. Okay and and here this has got large number of protons. So if you lose one proton gain one neutron lose one proton gain one neutron and registability curve.

[00:17:53]This this is what we call losing one proton and gaining one neutron. This is called beta plus decay. And this this this this we say in this particular case it will lose two neutrons because it has got large neutrons large protons and it will lose two protons. Again two neutrons two protons. So this is what we call this this is what we call alpha dk.

[00:18:07]So minor neat aspirin see beta decay when a nucleus this is nucleus z it is having mass number a zed is the atomic number basically it loses so this is basically in terms of beta minus dk we say an electron is coming out okay so we say electron is coming out that's why we call it the beta minus dk in terms of beta in case of beta minus dk we say mass number remains the same so atomic number increases by one you can understand it like this and when it comes to the beta plus dk so we say mass number remains the same and atomic number decreases by one you can keep it like this okay and in case of alpha decay my dear aspirins c nucleus will do the alpha decay we say in this particular case mass number decrees es by four because it is losing two uh four four particles in total two neutrons two protons so mass number decreases by two and atomic number decreases by sorry atomic number decreases by two mass number decreases by four and an alpha particle is coming out that's why we call it alpha decay so that's all for this my dear neat aspirants okay okay one more important thing over here we say recoil velocity of the daughter nucleus so we say in this particular case we say alpha when alpha decay takes place alpha particle when alpha particle comes out so what is the the the velocity of the daughter nucleus recoil velocity this is mass of alpha velocity of alpha divided by mass of the daughter nucleus you can keep it like this Okay, that's all for today. Thank you so much, guys.