 Tell me one thing, how much time it will take for a nucleus to go from N0 to N0 by 128, number of nucleus becomes N0 by 128, t half is given as 2 hours, get it quickly. So is it 14 hours? Others? Yes, so 14 hours. There you go, it will go from N0 to N0 by 2, in how much time all of you? T half. 2 hours, it is becoming half right, so it is half life from N0 by 2 to N0 by 4, again half, so 2 hours, N0 by 4 to N0 by 8, again 2 hours and then like this, it becomes a series. 2 hours, 2 hours and then N0 by 128, again 2 hours, so just count number of half lives, so this is 1, 2, 3, 4, 5, 6, 7, 7 to 2, 14 hours, getting it. So if you write this as N0 divided by 2 raised to power 7, so you can make out that this nucleus is becoming half, 7 times, so it will take 7 half lives, getting it. So be judicious about the calculation, don't just blindly start calculating. Now this, since we are talking about radioactivity, there are few particles which gets emitted other than nucleus, other than the daughter nucleus, few particles that gets emitted which are common across in different kinds of radioactive decay. So the name of radioactive decay is referred with respect to what kind of radiations are getting emitted. So there is an alpha decay, this is a decay in which helium nucleus gets emitted, in this helium nucleus gets emitted. I am not talking about helium atom, it is helium without any electron, so this is helium plus 2 that gets emitted. So it is quite common, so it is referred as alpha decay, whenever radioactive decay happens and alpha particle get emitted, we say that it is radioactive decay that is, sorry alpha decay that is going on. Then you have beta decay. In beta decay, you will see that electrons or positrons gets emitted. We will talk about it in some time, just write it down, electron or positron gets emitted from nucleus. This is little strange because nucleus doesn't have electron in it, then how come nucleus will emit electron and what is this positron? This we will discuss in some time right now, just write it down. Third, third type of decay is called gamma decay. So gamma is nothing but, it is photons, very high energy photons. In fact, there is a threshold, after that threshold, if you increase the frequency, you call it gamma ray beyond that. So there is gamma ray, which is considered to be the most energetic EM wave available in the universe. So this is what it is and this is a very high energy photon, it has very high energy and their energy is of the order of mega electron volt. The photon energy that we have discussed in atoms chapter is like few electron volts, like maximum energy for a hydrogen atom of a photon could be 13.6 electron volt that gets emitted when electron jumps from infinity to ground state. So 13.6 was the maximum energy that we have seen for hydrogen atom in atoms chapter. But here the photons we are talking about has one million times more energy than what we have seen in atoms chapter. They are very, very high energy photons and here just like when electron transitions from higher energy state to lower energy state and photons get emitted, here what happens? The nucleus transition from higher energy state to lower energy state. It is not electron that transitions, it is nucleus, entire nucleus transitions from higher energy state to lower energy state. This is what type of radioactive decay that are there. So I will quickly talk about I will take few examples of these kind of decay and then probably if time permits, although it is not likely. So what we will do? I will finish up these a few more topics and then we will have only problem solving session next class. Write down alpha decay. What happens in alpha decay? Helium nucleus comes out from the parent nucleus. So if I say that there is a nucleus Azx that becomes Y and it emits alpha particle which is 4 Hg2. What will be the atomic number and mass number of Y? A-4 and Z-2. This is what you will see. The mass number decreases by 4 and the atomic number decreases by 2. So can we find out how much is the energy that gets liberated from this reaction? Okay. Can we find out that? Suppose this is let us say a typical chemical reaction that is going on. So what we will do to find the energy that gets liberated? You subtract the enthalpy of formation of the product from the reactants. Isn't it? And that's how you get it. Yes or no? Yes sir. So here also if you subtract binding energies of Y, let us say this is binding energy of helium and this is binding energy of X. Okay. So if I take these two summations, if I say it is exothermic reaction then Y and helium will be more stable. So their binding energy will be more. So you just subtract Bex from these two summations. You will get the energy that gets liberated from here. Okay. So this is one way of finding the value of heat that gets liberated or what else you can do? Any idea quickly? You just find out the mass defect Mx minus My minus mass of helium. Okay. This is a mass defect. This into C square. Okay. So binding energy comes from mass defect only. So if you find out the difference in masses of these two from the product, that is a mass defect into C square will give you how much energy that gets liberated. Are you getting it? Yes sir. Okay. So that's two ways you can find out the energies here. So next, write down beta decay. So we could not take numericals, a lot of numericals today, but we'll have good amount of time we'll spend next class on just solving numericals. So meanwhile, you could solve a lot of questions yourself also. So beta decay will be of two types. Okay. This can be beta minus decay or beta plus decay. In beta minus decay, electron is ejected from the nucleus. Beta plus decay positron gets ejected from the nucleus. Positron has mass of electron and charge as negative of charge of electron. Electron charges one point minus 1.6 into times minus 19. So positron charges plus 1.6 into 10 is per minus 19. Fine. So the way it is different from proton is just mass. Mass of proton will be a lot higher. But charge of proton is same as charge of positron. Okay. So what happens is inside the nucleus, if neutron gets converted into proton, then it will emit electron and there is one other notorious particle that gets emitted, which is anti-neutrino. I'll just introduce anti-neutrino in some time. This is beta minus decay that is happening. A neutron from the nucleus gets converted into proton, electron and positron gets emitted. And in beta minus, for in beta plus, proton gets converted into neutron and a positron gets emitted with a neutrino. This is beta plus. This neutrino and anti-neutrino, they are very, very difficult to detect. In order to detect anything, you need to observe, you need to feel it or you need to have some instrument that can track the behavior or see indirectly what all changes happen if you apply in magnetic or electric field, things like that. But these neutrino and anti-neutrino, they are so notorious that they can just pass through entire earth without interacting with anything. So they are very difficult to detect. So for many years, nobody were knowing the existence of these particles. But later on, they came to know that such particles do exist. So you can see here clearly, if beta minus emission happens, let us say AXZ will give Y plus, let us say it gives out electron and anti-neutrino. So this is beta minus decay. So what happens to atomic number and mass number quickly? So mass number remains the same and atomic number increases by one. Exactly. Number of protons are increasing. So mass number is same, but atomic number goes up by one. So that's what. So nitrogen, if it goes with beta minus decay, what element it will become? Nitrogen will become what? Atomic number from seven, it becomes eight. What is eight? Oxygen. Oxygen. So nitrogen will become oxygen if it happens. And similarly, if it is beta plus decay, then what will happen to atomic number and mass number? See, inside the nucleus, neutron becomes proton, so atomic number goes up. Inside the nucleus, if proton becomes neutron, what happens to atomic number? 10 minus Y. It decreases. And mass number remains same. So in any of the beta decay, mass number remains same. So mass number doesn't change in beta decay. It is just atomic number that can go up or down. So beta minus atomic number goes up. Beta plus atomic number goes down. So remember this. Now write down gamma decay. So first, write down that gamma decay happens after alpha decay or beta decay. So it will not happen just gamma decay. Fine. It will be accompanied with alpha decay or beta decay. Okay? So when alpha decay or beta decay happens, then what happens after the decay? The nucleus becomes excited. So when nucleus is excited, its energy level becomes very high. So let us say in a reaction, beta minus emission cobalt 60, this will get transitioned into nickel 2860 if there is a beta minus emission. Fine. So after this emission, cobalt no longer remains in the ground state. It is in excited state. So this is the state of cobalt. Okay? What it does? It transition into different levels. So this cobalt, as I am sorry here, I am confusing between cobalt and nickel. So what happens cobalt after emission of beta minus, okay? When it emit beta minus particle, it becomes nickel. Fine. This nickel when it gets formed, this nickel is in excited state. Okay? What nickel does after forming, it emits a photon. Let us say the first photon is of the energy of 1.17 million electron volt. Then after that, it emits another photon. Okay? This energy is 1.33 million electron volt. Fine. And then you will get nickel in its ground state. Fine. So you can see that first cobalt has the beta minus decay, then it becomes nickel in the excited state. And after that, nickel goes to the ground state by emission of photons. And these photons, they have very high energy. And these high energy radiations, they are called gamma radiations. Getting it? Any doubts till now, whatever we have done till now? Okay. Just we will finish this session with a numerical. Write this down. You need to find out the amount of cobalt to provide, to provide radioactive source of 8 milli-curie strength. Okay? This much rate of disintegration should be there. The half life of cobalt is given as 5.3 years. You need to find in terms of, you know, grams. How many grams of cobalt will give you this much activity? Do it. Okay, guys. So are you able to solve this? Yes, I calculated. So what you do basically, dn by dt is 8 milli-curie, so 8 into 10 raise power minus 3 into what is 1-curie equals to 3.7 into 10 raise to the power, 10 raise to the power of 10. This should be equal to lambda times n. And lambda is what? 0.693 divided by t half, which is 5.3 years, which is this into 365, 24 hours, 60 into 60. So this multiplied with n. So from here you get number of nucleus, which is equal to number of atoms. Right? So for Avogadro number, you know that the mass is 60 grams roughly. Right? So for n atoms, you will get 60 grams divided by Avogadro number into n grams. Is it clear, all of you? 7, 6 grams. 6.6 into? 10 to the power negative 6 grams. Okay. This is I think 13.9 question number from your NCRT book. You can directly refer that and in case you have not got it from here, just text me, I will reply back to you. Okay, so the homework is you need to finish entire HCRMA and come up with your doubts next class. And if time permits, go beyond HCRMA, solve that book that is with you and we will discuss doubts and we will solve questions during the first two hours of the session, next session. Okay.