 Hello everyone. So in the previous lecture, we discussed about the discovery of nucleus, proton, neutron and also how the idea about the nuclear radius was obtained from experiments on scattering of high energy electrons and other heavy charge particles by the nuclei. We also discussed about the nuclear mass and binding energy. Now, we will discuss what are the factors that govern stability of nuclei. So, a very simple way of explaining is to see the frequency distribution of stable isotopes that gives an idea. So, what I have made here is a table containing the different configurations of protons and neutrons substituting nuclei. So, mass number even mass number can come from even z and even n and there are 165 nuclei which are stable having even even configuration. For example, helium 4, carbon 12, magnesium 24 and so on. So, these nuclei have even protons even neutrons. We will call them even even nuclei. We can also have even mass number from ordered configuration. That means odd proton odd width. And you will see there are only 4 nuclei which are stable having ordered configuration like deuterium lithium 6, boron 10 and nitrogen 14. This is a very, this is a, this gives an idea that the nucleons tend to be paired up. They like to remain paired up. So, the majority of the stable isotopes are of even even type and there are only 4 nuclei which are of ordered type. Therefore, pairing energy plays a very important role in the stability of nucleus. Second point is if you see the table, nuclear table, nuclear chart, how many isotopes, stable isotopes a particular element have, you will find the certain elements having mass number, atomic number 20, 20 is your calcium, tin, lead, they have a very large number of stable isotopes. So, it essentially tells us that there are certain magic numbers which have extra stability associated with these numbers. And later on we will discuss that the magic numbers are 2, 8, 20, 50, 82, 126. So, if a nucleus has got 2 protons, 8 protons, 20 protons or it has got 2 neutron, 8 neutron, 20 neutron and so on, certain nuclei have extra stability. So, one is that nucleus, some certain magic numbers are more stable and also the nucleons like to remain paired. So, that gives you stability to the nucleus. Another important property governing the stability of nucleus is the neutron to proton ratio, n by that ratio. So, what I have shown here in this graph is the number of neutrons and number of protons for stable nuclei. This distribution gives you how these stable nuclei are distributed in regard to proton number and neutron number. And I have drawn a line where n equal to z. So, you see here up to proton number 20 n equal to z. That means up to calcium 40, 20 proton, 20 neutron, calcium 40, up to this mass number 40, equal number of neutron and proton can make the nucleus stable. The moment we go more than calcium, more than proton number 20, you require more neutrons to stabilize the nucleus. You can see here for 40 protons, you require close to 50 neutrons. For 60 protons, you require close to 90 neutrons. You can see here as you increase the number of protons, the number of neutrons to stabilize the nucleus increases further. So, for stable nuclei with the z more than less than or equal to 20, neutron to proton ratio is equal to 1. But for those nuclei which are stable having z more than 20, then they have got certain excess neutrons. So, as we increase the proton number in the nucleus, you require more neutron than proton to stabilize the nucleus. And the heaviest nucleus that is stable is 209 bismuth that is n equal to 126. Beyond this 209 bismuth, then all radium nuclei are unstable. So, both the certain magic numbers help in stabilizing nucleus, nucleon, the pairing energy helps if the nucleons are paired up, that nucleus is more stable. And it has to be the neutron to proton ratio has to be in certain range to make the stable nucleus. Now, so what holds this neutron to proton tightly inside a nucleus? So, that is the what is the force that is operating between the nucleon. So, we will use the term nucleon to represent both protons and neutrons in the discussion. Because the in fact, we will see later on that nuclear force is independent of the whether it is proton or neutron, it is charged in different. So, we saw that we will see we will see this very soon that the nuclear force is short range, it operates at a very small distances of the order of fermis, it is attractive to nucleon node. That is how the nucleus remains, it is spherical nucleus, the nucleons try to attack each other over a very short range. So, then the neutron proton behaves similarly with regard to nuclear force, but that is why we call them as nucleons. Neutrons and protons are spin half particles, so they are called as fermions. Spin half particles are called fermions and spin 1 are called bosons, one integral spins are called bosons. So, the nuclei having spin half integral half integral spins will follow Fermi Dirac. We will also discuss later on the implications of these discoveries in 1929 Paul Dirac in UK predicted that electron has an antiparticle which he called as the positron. In fact, the thesis by Paul Dirac is a very small thesis wherein he solved the equation of state of electron and predicts that this has got two solutions, the positive solution is electron and so negative solution is antiparticle of electron which is called as positron and subsequently in 1932 CD Anderson discovered the positive. So, gradually we will see that every particle every nuclear particle has an antiparticle and which becomes important in explaining many observations. So, till now what we have understood that any matter is composed of electron, proton and neutron and therefore, we say that these three particles are the elementary particles of matter. Any matter is made of these are the fundamental part, fundamental part of building blocks of all matter. Later on at the end of this lecture as the time permits I will also show that there is much more than this. So, let us go into further. So, what holds the nucleons together in the nucleus? In 1935, Yukawa gave the exchange theory of pie missiles. So, he proposed that inside the nucleus the protons and proton or proton, proton, neutron, neutron are exchanging a particle which he called as the meson and so, it is like two players playing volleyball. So, if the volleyball is exchanged very fast you will see like a banana between the two players and that binds the two two. Similarly, in this a proton gets converted into a neutron and pi plus positive pi meson and then this positive pi meson. So, it is actually this is from the proton and later on this neutron captures this pi plus meson to get neutron and proton pair. So, this is how a neutron and proton exchange, a proton becomes pi plus plus neutron and so. Similarly, a neutron can convert become pi plus proton and pi minus and this pi minus is captured by proton give you neutron. So, neutron proton exchanging pi minus meson again become proton neutron and the proton and proton will exchange a neutral pi meson and the neutron and neutron will exchange neutral pi meson. So, they are constantly exchanging these pi mesons between them a pair of nucleons will exchange a pi meson depending upon whether it is proton neutron or neutron proton or proton proton the charge of the pi meson will be different. The masses of these pi mesons are given here pi plus meson pi minus and pi neutral they are charges and they are half-life. So, they have very short half-life particles they do not survive for long time. Now, the inside that nucleons in nucleus when this pi meson is released from one proton it is survives for a very short time and based on the time of survival you can calculate how much distance it will travel within this much time and that gives you the range of nuclear. So, the range of nuclear force happens to be of the order of one hermit and you will see the corollary of this the important point is that how we are able to produce a particle of 140 MeV between a proton and neutron when the they are remaining intact a pair of proton neutron we remain proton neutron pair, but in the process generate a mass of 140. Does it not violate the law of mass energy conservation? Apparently, you feel that it is not possible to generate mass from a pair of proton neutron and they are remaining intact, but then that is where the Heisenberg-Artsonary principle comes to our rescue. The Heisenberg principle of energy and time this product of delta E into delta T has to be more than referred to the Langston constant h cross h by 2 pi and from this you can predict that if you produce a mass certain mass number. So, 140 mass you can do the exact energy then you can see it will survive for a time which is possible by complying with the Heisenberg principle. So, that explains that that is how we could explain that the pi meson exchange theory is valid because this pi meson does not survive it is captured by another nucleon inside the nucleus and so this is how what forms the bond between the nucleons inside that nucleus. So, to list the different properties of this nuclear force and later on we will see how we can when we make a model to explain the different properties of the nucleus this nuclear force properties will become useful. So, what we found out from the previous discussion about the frequency of stable nuclei we found that the nuclear force is charged in the. How do we say that we found that the even proton or even proton or proton or proton even neutron there are the number of stable nuclei are nearly same 55 and 50 if you recall the table of table isotopes that even proton or neutron 55 even neutron or proton 50. So, the number of stable nuclei having even odd or odd even configuration is nearly same that means the nuclear force is charged independent that means NP or PP or NP exchange is of the same order. The second property of this nuclear force is that it is spin dependent and the evidence for this came from the ground state of deuterium. The ground state of deuterium is a triplet stable in deuterium has one proton and one neutron. Now, proton and neutron can be paired up or it can be unpaired what is found that the ground state is paired in a ground state they are unpaired and the unpaired the paired state is unstable. So, that means if the two nucleons in the nucleus are having depending upon the state the spin state of the two nucleons nucleus can be stable or unstable that gives an idea that the nuclear force is spin dependent. Third property is nuclear force is short range at just we just discussed this just now that the mass of the pi meson which is 140 MeV which is surviving for 10 power minus 24 seconds. So, what is the range of nuclear force the distance travelled by pi meson within this time assuming that it is moving velocity of light so velocity into time so we have 10 power minus 15 meter. So, it is a short range it operates at the permies and that is why you know when you will say the nucleus dimension 10 Fermi then it is not operating at 10 Fermi it is optic at 1 Fermi and that is why each nucleon is in fact only with those nucleons which are in the immediate vicinity of it that there comes the property of saturation. So, the binding energy per nucleon or the average binding energy is constant that means every nucleon is interacting with only those nucleons which are in its immediate vicinity so that calls the saturation of the nuclear force. So, the saturation of nuclear force also it comes out from the constancy of the average binding energy. There are other properties of the nuclei other than the nuclear force is which we will discuss later on is nuclear spin. So, every nucleus because neutrons have spin half protons have spin half and nuclei have spin it can be half integral or it can be integral. So, if it is an odd mass dump, nucleus is odd mass that means either protons are odd or neutrons are odd then this nucleus will have half integrals spin. If it is an even mass nucleus it could be even proton even neutron or odd proton or neutron then this nucleus will have integral spin and in that also if it is even even nucleus then i equal to 0. If it is odd odd nucleus then i is equal to some. This is for the ground state of the ground state spin of nuclei follows this. There are other properties nuclei have their magnetic moment magnetic dipole moment. So, the magnetic dipole moment comes from one is the spinning of the proton and neutron along its own axis. So, if a proton spins like electron has a Bohr magneton, nuclear proton has got a nuclear magneton E h upon 4 pi mu m m n. So, not only the spin spinning of the proton and neutron gives you the magnetic moment of proton and neutron, but the orbital motion of proton will also give you its magnetic dipole moment, but not that of the neutron. So, important point is that the neutron has got a magnetic dipole moment when it is spinning around its own axis and that gives tells lot about whether the neutron, proton are fundamental particles or they have certain structure. So, proton has got a magnetic moment of 2.79 nuclear magneton, neutron has got minus 1.91 nuclear magneton. So, nuclei are magnetic particles you must have read about nuclear magnetic resonance where the magnetic dipole moment interacts with the supply around magnetic field gives you the splitting of the levels. Similarly, nuclei have what you call as the electric quadrupole. The electric quadrupole moment comes from the asymmetric distribution of charge the nucleus. So, if the nucleus is having a distribution like if it is can be a prolate or oblate having semi-measure and semi-measure axis a and b then we can this is a classical parabola for quadrupole moment, but you can have it from the electron the nuclear charge distribution inside nucleus you can calculate the quadrupole moment of the nucleus and there are techniques the hyper sign interaction based techniques whereby one can experimentally find out the magnetic dipole moment electric quadrupole moment. So, these are the properties nuclei possess nuclei also follow certain statistics for half integral nuclei will have Fermi Dirac or integral spin will have the Bose Einstein statistics and they also have parity. So, parity is nothing but the reflection symmetry. If you change the wave function from x to minus x if the wave function changes sign you say it is odd parity it does not change the sign we say it is even better. So, nuclei also have parity we will discuss this parity when we discuss the spin states of nuclei. Now, I just told about the proton and neutron and electron are elementary particles till 19 early 1930s it was all very well accepted, but then what happened the so we can say that the type of particles of which the other matter is made of is proton, neutron and electron. But in the 1930s and 40s in accelerators as we had high energy accelerators and even in the cosmic rays different types of particles are formed and they were called as the strange particles. These strange particles could not be explained in terms of the neutron, proton and electron. And there is a very detailed experiments have been done in the for the last so many years. I will not go into details of these different discoveries, but what happens here I give you a list of particles apart from neutron, proton, there are other particles lambda, sigma, delta and so on. And these particles are also like proton, neutron, but their masses are higher. And there were also particles apart from pi meson, there were k mesons, there are rho mesons and they are they are they were discovered experimentally in the cosmic rays or even in the accelerators later. Similarly, apart from electron there are neutrinos, there are mu mesons, there are meonic neutrinos, there are tau meson, tau particles not mu meson, muon and there are tau lepton. So, tau lepton. So, there are different types of particles which were discovered subsequently and so it was it was known there is a doubt whether proton, neutron are the fundamental element to particles. And so they were there was a classification of these different particles into hydrons. Hydron means which are interacting by strong interaction and the baryons are this spin half particles and half integral spin particles, neutron, proton, lambda, delta particles. Then the mesons are actually integral spin particles. So, they are made of certain things which we will discuss very soon. And these are the leptons, light particles lepton means light particles which are interacting by weak interaction. So, we have particles interacting by strong interaction, particles interacting by weak interaction and there that is how the scientist started feeling that proton, neutron may not be the fundamental particle building blocks of matter. And therefore, in 1964, when a good number of discoveries of strange particles have happened, 1964, Murek Gelman and Zwick predicted this is one of the you know where the theory precedes the experimental evidence. So, these two scientists predicted independently that the protons and neutrons and different baryons. So, when we said baryons, baryons are made of strong interesting particles and they are made of quarks. So, the quark concept quark structure of nucleus nucleons was proposed by Gelman and Zwick and these quarks are of different type, they are called a different flavors and different colors. So, we have up quark, down quark, up quark, down quark, charm quark, strange quark, top quark and bottom quark and each quark when it is inside a nucleon or a particle, it can have different colors, red, green. So, that is only for the understanding, they do not really have that color, but to explain certain properties, you give them some nomenclature. So, these quarks are having different colors, different flavors, colors and they have different charges also. So, the first time there were particles having fractional charges, we have not heard about fractional charge. So, up quark, charm quark and top quark were proposed to have plus 2 by 3 charge and the down quark, strange and bottom was to have minus 1 by 3 charge and it was experimentally later on you can prove that a proton is made of UUD, 2 up quark and 1 down quark. So, you can see up quark is plus 2 by 3, plus 2 by 3, minus 1 by 3 for d quarks, the charge of proton is plus 1. Neutron is UDD, 1 up quark and 2 d quark, plus 2 by 3, minus 1 by 3, minus 1 by 3, 0. So, it could explain the charge, not only the charge, the spins and many other properties of the nucleons, so not nucleon, they are called baryons. Apart from proton-neutron there are other particles, lambda, delta, sigma particles, all of them could be explained and they have been all discovered this time. Another types of particles are leptons means light particles and they are not made of quarks and they participate in the weak interactions and not in the strong effects. So, these 6 leptons are having electron, muon, tau having minus 1 charge and they are corresponding neutrinos, electronic neutrino, meonic neutrino, tau neutrino, zero charge. And these are very small particles they have very less mass 0.511 MeV4 electron, muon and tau lepton. And then their corresponding neutrinos are still much lower masses. In fact, still there are experiments going on to find out the mass of neutrino. So, it is predicted that the electronic neutrino will have about less than 30 electron volt mass, meonic neutrino less than 0.25 millilectron volt and tau neutrino less than 70 millilitres. So, there are experiments going on to find out the masses of the leptons. So, leptons that means these light particles like electron and neutrino, they are involved in beta decay and other weak interactions. We will see later on how the beta decay of a neutron gives you electron and anti-neutronome and the beta decay of a bound proton gives you positron and the neutrino. So, these are the kind of observations which have been made which now this is a domain of hydrodiphygics. So, I will not go into the details of this particular area, but just to give you a feel that apart from neutron proton and from there are now many, many other particles which have been discovered and the scientists are trying to in fact explain all the particles that are discovered in hydrodiphygics, heavy ion reactions, hydrogen reactions or even in the cosmic range. So, there are many, many particles which are been observed and they have been now explained in terms of 6 quarks and 6 leptons. So, apart from the nuclear physics which deals with proton, neutron and electron, there is another domain of nuclear science that is hydrodiphygics where one deals with the other particles which are baryons, leptons and undergoing strong and weak interactions. That is all I had to say. Thank you very much.