 Yes sir. What you did last week? Yes sir, I completed HCE Verma. I couldn't do the lecture thing because of the exam right now. Okay, so you don't have any doubts? Not really sir. And who else? 34th one. 34th, you have sent me? Yes sir. This is from HCE Verma is it? Yes sir. Okay, so we have a small plate having work function phi which is kept at a distance d from a singly ionized fixed ion. Okay, fine. So at a distance d there is an singly ionized. Singly ionized means what? Its charge is charge of an electron. Okay, so this is a positive charge kept at a distance d from a metal surface having work function phi. A monochromatic light beam is incident on the metal plate. Okay, so photons are hitting this plate. Find the maximum wavelength of the light used so that some of the photoelectron may go around the ion along the circle. Okay, so let's say the wavelength is lambda. So the energy of the photon will be what? HCE by lambda. Right? Now if work function is phi what will be the kinetic energy of the electron that will be emitted out from the metal surface? HCE by lambda minus phi. Correct, so HCE by lambda minus phi. This will be the kinetic energy. This is the maximum kinetic energy of the electron that will be coming out. This will be equal to what? Half m into v square. This is your first equation. Fine, so if the electrons that are coming out have to move in a circle then the complete velocity should be in the direction which is perpendicular to the direction of the force. Because this is the force of attraction from this charge which is equal to what? Force of attraction will be equal to KQ which is charge of electron multiplied by the electrons charge divided by d square. Okay, so this force should be equal to mv square by d. Okay, I am assuming that velocity of the electron coming out is perpendicular to this force. So it becomes tangential velocity and if it has to move in a circle then it should have a centripetal acceleration v square by r. And to provide that acceleration there has to be a force and that force is this force of attraction. Is it okay? Yes, sir. No doubts? Fine, let us move to this chapter. Write down nuclei. Now we have a brief discussion of nuclei when we were discussing about Rutherford experiment in the atoms chapter, isn't it? So we have this understanding now that at the center of the atom there should be a positively charged and very small object. So this positively charged and very small object, this thing is called nucleus. So you might have brief understanding about the nucleus already maybe from your chemistry chapter or you might be already knowing about the nucleus. So we will not assume any prior knowledge about it. So we will build it from the scratch. So Rutherford have conclusively proved that at the center there is this positively charged particle that is residing and it is very, very small. So in fact it is that small that the radius of this object is 10 raise to power 4 times the radius of the atom. So if you talk about the volume wise, the volume of this nucleus will be of what factor? 10 raise to power 12. It will be cube times smaller. So this will be V0 divided by 10 raise to power 12. Now you can sense how small the nucleus is. So it is the volume of atom divided by 10 raise to power 12 which is very, very small compared to the size of the atom. So we are dealing with a very tiny object and why this is very important? Because 99.99% of the mass resides inside it. 99.99% of the mass of atom is inside this very, very small volume. So that is why it is so important. Now during those times when nucleus was first discovered, they were also of the opinion that inside the nucleus there will be electrons also. But then using some quantum physics argument, it was proven that the atoms are inside the nucleus, electrons are not possible. So since then on it was assumed that inside the nucleus there will be only positively charged particles. And these positively charged particles, they were referred as protons. So it was during that point in time when manly, when this modern periodic table was getting built, it was also observed that the chemical property of any atom depends on how many protons are there in the nucleus. So this is a good measure or good, so to say, you can, knowing how many number of protons are there, you can actually estimate what will be the chemical property of an atom will be. So also number of protons will be equal to number of electrons also. So when you say that you are assuming that the atom is not ionized. So in a neutral atom, so number of protons will be equal to number of electrons because net net the charge should be zero. So for a long time it was assumed that inside the nucleus only protons are there. But then Chadwick did some experiment in 1932. So there was a big gap of around 20 years. People were unaware of this particle called neutrons. So in 1932 what Chadwick did, he bombarded alpha particle onto beryllium atom. So when he bombarded alpha particle into beryllium atom, he has observed a stream of neutral, he observed there was this neutral wave that was coming up. So this wave when it was coming up, people thought that it is an EM wave and it is neutral. How will you judge whether it is neutral or it has some charge? You just apply some sort of magnetic field or electric field if there is a deviation. To the stream of particles, then you can understand that it has some charge. Because electric or magnetic force can be only applied on some charged objects. Neutral objects won't feel any electric or magnetic force. So it was understood it is neutral. But then that point in time, EM wave was considered to be a well-known neutral wave. So when this neutral particle wave was used to ionize some atoms, let's say hydrogen atom. So it can knock out few electrons from the hydrogen atom and it can get ionized also. So using that and using conservation of energy and conservation of mass, there was this understanding that it is not a photon. So it must be some sort of particle that is coming out from the atom. So that's how people came to this understanding that inside the atom there are these neutral particles also. And these neutral particles, they were referred as neutrons. These are neutrons and protons were known beforehand only. So let's represent protons as P and neutrons as capital N. So both proton and neutron, they reside inside the nucleus. So this was an understanding that inside the nucleus there are protons and neutrons that are residing. And since the nucleus consists of almost entire mass, so the mass of the atom is nothing but more or less same as the mass of the nucleus itself. But then the mass which we are dealing with is very, very small. Like the mass of proton, if you try to find out, it will be around 1.67 into 10 raise to power minus 27 kg. So it's a very, very small mass. So there is a need to define a small unit of mass so that it becomes convenient for us to write down the atom's mass as such. Just like we have a unit of electron volt when we talk about energy, we have something called as atomic mass unit AMU to represent what is the mass of an atom. So this unit gets introduced to talk about the mass of the atom. And since like any other unit, we need to first assume how much is one unit of it? Like one AMU is what? So the way it is defined is like this. One atomic mass unit or let us say just one unit is nothing but one-twelfth of the mass of C12 atom. Why it is referred C12 atom? Because carbon can have isotopes. We'll come back to isotopes a little bit later. Right now, just write down this definition. This is the definition of one unit of the mass. And carbon 12, the mass of that is 1.992 into 10 raise to power minus 26. So this is the mass of one carbon 12 atom. So one unit this much kg. When you talk about one unit, mass of one unit, that will be what? This divided by 12, 1.992 divided by 12 into 10 raise to power minus 26 kgs. So one unit will come out to be around 1.66 into 10 raise to power minus 27 kgs. So like this, we have a new unit to talk about what is the mass of the mass of any atom. Any doubts till now? I'll assume no.