A Boot Camp to Nuclear Physics

The Avogadro constant is the proportionality factor that relates the number of constituent particles in a sample with the amount of substance in that sample. Its SI unit is the reciprocal mole, and it is defined exactly as NA = 6.02214076×10²³ mol⁻¹. 1amu=1.660539068×〖10〗^(-27) kg=931 MeV.

Mass of the atom is concentrated in the nucleus, which is at the center of the atom. As discussed earlier, nucleus is constituted by neutrons and protons. It has been observed that the mass of the nucleus is always less than the sum of the masses of all nucleons present in the nucleus. The difference in the sum of masses of all the nucleons present in the nucleus and the nuclear mass is known as the mass defect

Mass defect does not convey much information about nuclear stability, and it is misleading to say that higher the mass defect, more tightly bound nucleons exist in the nucleus.

This missing mass may be regarded as the mass, which would be converted into energy if a particular atom is to be formed from the requisite number of electrons, protons, and neutrons. This is also equal to the amount of energy required to break up the atom into its constituents. Therefore, the mass defect is a measure of the binding energy of an atom. The more the mass defect, the more tightly the nucleons are bound in the nucleus.

A better measure is the binding energy per nucleon , which is the ratio of the binding energy of a nucleus to the number A of nucleons in that nucleus. Here we will analytically discuss the issue for various mass number and conclude the possibility of energetically advantageous fission and fusion process.

In the periodic table, there are nuclei, which are called stable, i.e. the properties of these nuclei do not change with the passage of time unless the nuclei are otherwise disturbed. Yet there is another class of nuclei, whose number is much more, which are unstable. They disintegrate spontaneously by emitting either electromagnetic radiation or some particles. The phenomenon of spontaneous decay of a nucleus accompanied by the emission of alpha-particles, beta-particles, or gamma-rays is known as radioactivity. The present lecture describes the nuclear disintegration model.

Although we cannot predict which nuclei in a sample will decay, we can say that if a sample contains N radioactive nuclei, then the rate (=-dN/dt) at which nuclei will decay is proportional to N. The law is in the form of differential equation which is solved in this lecture.

There are two common time measures of how long any given type of radionuclides lasts. One measure is the half-life of a radionuclide, which is the time at which both N and R have been reduced to one-half their initial values. The other measure is the mean (or average) life t, which is the time at which both N and R have been reduced to 1/e of their initial values.

As we have seen that infinite time is required for the complete disappearance of the radioactive material, one does not know which atom of the material is going to decay at a given instant of time, i.e. individual atoms have lifetime from zero to infinity.

The graphical representation of (i) disintegration rate with time and (ii) number of radioactive nuclei nuclide with time offers a better look at half-life and life span. Maple 2020 software is explored to handle equations and plot graph.

In this process, the parent nucleus disintegrates to give a daughter nucleus and helium nucleus or an α-particle. The law of successive disintegration is discussed followed by estimation of the Q-value & properties of α-particles.

In this process, the parent nucleus disintegrates to give a daughter nucleus and helium nucleus or an α-particle. Due to this variation in the number of electron-ion pairs produced that the straight line gets broadened. The actual experimental α-particle spectrum in the decay of 241Am i.e. Americium is discussed in detail. The mass number of the daughter nucleus decreases by four units and the atomic number decreases by two units. In this lecture range of alpha particles and Geiger-Nuttal law is described.

A nucleus that decays spontaneously by emitting an electron or a positron (a positively charged particle with the mass of an electron) is said to undergo beta decay. Like alpha decay, this is a spontaneous process, with definite disintegration energy and half-life.

In the process of beta law of conservation of charge was obeyed while the law of conservation of energy, momentum, and spin was violated that puzzled N Bohr however in 1931 Pauli proposed neutrino hypothesis that sorted all laws of conservation and later on the existence of Neutrino was confirmed experimentally. Beta-decay processes are threefold neutron decay, proton decay, and electron capture which are elaborated in this lecture.

Alpha and beta decays of a radioactive nucleus usually leave the daughter nucleus in an excited state. If the excitation energy available with the daughter nucleus is not sufficient for further particle emission, it loses its excess energy by the following processes:

1. Gamma decay.

2. Internal conversion.

3. Internal pair conversion.

The effect of radiation such as gamma rays, electrons, and alpha particles on living tissue (particularly our own) is a matter of public interest. Such radiation is found in nature in cosmic rays (from astronomical sources) and in the emissions by radioactive elements in Earth’s crust. Radiation associated with some human activities, such as using x rays and radionuclides in medicine and in industry, also contributes.

There are two remaining quantities of interest.

1. Absorbed Dose and 2. Dose Equivalent.

The drop of liquid composed of molecules has a great resemblance with the nucleus composed of nucleons (protons & neutrons). This analogy has been discussed in this lecture to develop the grounds for liquid drop model.

The analogy developed on the grounds of similarities between the drop of liquid and nucleus opens the discussion for the binding energy due to volume suppressed by contribution due to Surface, Colombian (repulsion amongst Z protons) followed by asymmetry and pair contribution. This lecture develops arguments for the writing of semi-empirical formula which is in good agreement with the binding energy per nucleons Vs mass number.

The Shell Model of Nucleus is somewhat similar to the Atomic structure, in the sense that electrons that revolve around the nucleus in an Atom do so in discrete Energy levels / or Shells, wherein filling up of certain electron Shells leads to the exceptional stability of the chemical elements. Such electronic configurations are known as Inert Gases or Noble Elements like helium, neon argon krypton, and so on. These configurations correspond to certain atomic numbers. A similar concept also exists in the case of the Nucleus. There are certain numbers associated with the number of neutrons/ protons in a nucleus that has very interesting properties. These numbers are called Magic Numbers. Magic Numbers: 2, 8, 20, 28, 50, 82, 126 Any nucleus which has the number of neutrons/ protons that correspond to the Magic Numbers show exceptional nuclear stability, and abundance in nature.

Nuclei are more complicated than atoms. For atoms, the basic force law (Coulomb’s law) is simple in form and there is a natural force center, the nucleus. For nuclei, the force law is complicated and cannot, in fact, be written down explicitly in full detail. Furthermore, the nucleus—a jumble of protons and neutrons—has no natural force center to simplify the calculations.

In the absence of a comprehensive nuclear theory, we turn to the construction of nuclear models – The Fermi Gas Model. A nuclear model is simply a way of looking at the nucleus that gives physical insight into as wide a range of its properties as possible. The usefulness of a model is tested by its ability to provide predictions that can be verified experimentally in the laboratory.

A particle accelerator is an instrument used to increase the kinetic energy of charged particles such as electrons, protons, alpha particles, and other heavy ions.

In this video lecture, we are going to learn the basics of how a particle is accelerated through a potential difference. This concept is explored in a repetitive way in different devices.

A linear accelerator (LINAC)accelerates charged particles to high energies without the need for very high voltages. In linear accelerators, there are a series of coaxial hollow cylindrical electrodes, known as drift tubes to which an alternating voltage is applied. Successive tubes have opposite voltages, but the voltage alternates with the frequency of the applied voltage. If the lengths of the tubes are correctly chosen, the motion of the charged particles is synchronized with the alteration of the voltage so that they cross the gap between the successive tubes at the right time to receive a push that increases their energy. A wonderful animation of Linac is displayed on the last slide.

Beams of high-energy particles, such as high-energy electrons and protons, have been enormously useful in probing atoms and nuclei to reveal the fundamental structure of matter. Because electrons and protons are charged, they can be accelerated to the required high energy if they move through large potential differences. The required acceleration distance is reasonable for electrons (low mass) but unreasonable for protons (greater mass). A clever solution to this problem is first to let protons and other massive particles move through a modest potential difference (so that they gain a modest amount of energy) and then use a magnetic field to cause them to circle back and move through a modest potential difference again. If this procedure is repeated thousands of times, the particles end up with considerable energy. Here in this video lecture, we shall discuss accelerators that employ a magnetic field to repeatedly bring particles back to an accelerating region, where they gain more and more energy until they finally emerge as a high-energy beam. The cyclic acceleration is caused by potential difference that leads us to a device known as CYCLOTRON. 

A betatron is a type of cyclic particle accelerator. It is essentially a transformer with a torus-shaped vacuum tube as its secondary coil. An alternating current in the primary coils accelerates electrons in the vacuum around a circular path. The betatron was the first machine capable of producing electron beams at energies higher than could be achieved with a simple electron gun, and the first circular accelerator in which particles orbited at a constant radius. The first working betatron was constructed by Donald Kerst at the University of Illinois Urbana-Champaign in 1940. In a betatron, the changing magnetic field from the primary coil accelerates electrons injected into the vacuum torus, causing them to circle around the torus in the same manner as current is induced in the secondary coil of a transformer (Faraday's law). In the present video lecture, we shall learn the construction and working of Betatron.

In both atomic and nuclear burning, the release of energy is accompanied by a decrease in mass, according to the equation Q=-∆m c^2. The central difference between burning uranium and burning coal is that, in the former case, a much larger fraction of the available mass (again, by a factor of a few million) is consumed. The different processes that can be used for atomic or nuclear burning provide different levels of power or rates at which the energy is delivered. In the nuclear case, we can burn a kilogram of uranium explosively in a bomb or slowly in a power reactor. In the atomic case, we might consider exploding a stick of dynamite or digesting a jelly doughnut.

The nuclear cross-section is a convenient way to express the probability that a bombarding particle will interact in a certain way with a target particle. Hence, the greater the cross-section, the greater the likelihood of interaction. The nuclear cross-section is usually denoted by σ.

There are many ways of classifying nuclear reactions. Two commonly used ways

to classify nuclear reactions are:

1. Reactions based on the reaction mechanism.

2. Reactions based on the mass of the projectile.

In nuclear reactions, certain physical quantities never change during and after the reaction. We say that these quantities are always conserved in nuclear reactions. Some of the conservation laws are discussed in this video lecture.

In any nuclear reaction, laws of conservation of energy and momentum always hold good. These conservation laws impose certain conditions on nuclear reactions like that the energy of the outgoing particles must be real, etc. These restrictions are called kinematical restrictions and the mathematical relations derived by imposing these restrictions are known as kinematics.

Nuclear fission is a process of splitting a nucleus, generally, a heavy atom (target) into two or more lighter atoms (fission fragments) when it is bombarded by neutrons or charged particles. A few radioactive nuclides can also spontaneously fission such as 254Cf and 256Fm. Fission releases a large amount of energy along with one or more neutrons.

Otto Hahn discovered in 1938 that when uranium was bombarded with thermal neutrons, the uranium nucleus broke up into barium and krypton nuclei of atomic numbers 56 and 36 and liberated 3 neutrons accompanied by a tremendous amount of energy.

This lecture will enable you to estimate the energy released by the fission of a high-mass nuclide by examining the total binding energy per nucleon before and after the fission. Soon after the discovery of fission, Niels Bohr and John Wheeler used the collective model of the nucleus, based on the analogy between a nucleus and a charged liquid drop.

The Sun has been radiating energy at the rate of 3.9*10^26 Watt for several billion years. Where does all this energy come from? It does not come from chemical burning. (Even if the Sun were made of coal and had its own oxygen, burning the coal would last only 1000 y.) It also does not come from the Sun shrinking, transferring gravitational potential energy to thermal energy. (Its lifetime would be short by a factor of at least 500.) That leaves only thermonuclear fusion. The Sun, as you will see, burns not coal but hydrogen, and in a nuclear furnace, not an atomic or chemical one. The fusion reaction in the Sun is a multistep process in which hydrogen is burned to form helium, hydrogen being the “fuel” and helium the “ashes.” In this video lecture, we shall learn how nuclear fusion becomes a source of stellar energy.

A nuclear chain reaction is a self-propagating process in which the number of neutrons goes on multiplying rapidly almost in geometrical progression till the total fissionable nuclei in the material are fissioned. This process leads to an uncontrolled progression of Nuclear Reactions. For wise use of nuclear energy, such nuclear reactions need to be controlled. The external mechanism that envisages desirable control of Nuclear Reactions so that explosive conditions are averted leading to apt use of the energy for the desired purpose is achieved through Nuclear Reactors. The present video lecture is rendering brief information about such Nuclear Reactors.

Radioactive decay and nuclear reactions are accompanied by the emission of charged particles like alpha-particles, beta-particles, protons, and gamma rays. Our senses cannot detect these products directly, and detection must be done by indirect means. More immediate and quantitative methods of detection are desirable and a variety of instruments have been developed for this purpose. Some of the common radiation detectors and mass spectrometers are described in this Section 7. This video lecture stating Introduction describes a classification of detectors and some basic phenomenon that are explored in the fabrication of these detectors.

GM Counter is a detector that is capable of detecting alpha, beta, and gamma particles along with protons. When an ionizing particle passes through the gas in an ionizing chamber, it produces electro-ion pairs. If the applied potential difference is strong enough, these ions will produce a secondary ion avalanche whose total effect will be proportional to the energy associated with the primary ionizing event. But the issue is not as simple as it is said. The present video lecture describes the working principle, construction, and working of GM Counter along with the various phenomenon around that include quenching, self-quenching, counting, dead time, recovery time, paralysis time.

It is one of the detectors, which provides a visual trajectory of a charged particle like an electron, proton, alpha-particles, etc. Cloud chamber also known as Wilson Chamber was built by C.T.R. Wilson in 1911 at Cambridge. It is based on the principle that when dust-free air saturated with vapors of a liquid (like water, alcohol, ether, etc.) is allowed to expand adiabatically, supersaturation occurs. If at this stage an ionizing particle enters the chamber and creates ion pairs, tiny droplets of liquid condense on these ions and form a visible track along the path of the ionizing radiation. The present video lecture describes the working principle, construction, and actual working of Cloud Counter along with some interesting photographs that enable the viewer to approach analyze nuclear particles using Cloud Chamber.

We are familiar with ZnS screen used by Rutherford in his famous scattering experiment. a-particles, when falling on ZnS, produce light flashes or scintillations. These flashes can be seen with a microscope. ZnS was the first scintillation detector put to actual use.

Like ZnS, other scintillating materials include; sodium iodide, cesium iodide, anthracene, naphthalene, etc. Some gases particularly noble gases like xenon, etc. also exhibit this property. Scintillation detectors became the most powerful and widely used radiation detectors with the development of photomultiplier (PM) tubes. A scintillation spectrometer consists of three components; 1. Scintillation detector/crystal, 2. Photomultiplier tube, 3. Electronic circuitry.

The present video lecture describes Construction & Working along with the Advantages & Limitations of Scintillation Counters.

The basic drawback of cloud chamber is that because of the low density of the gas, it is not possible to observe high energy particles. In 1952, D.A. Glaser at the University of Michigan, conceived the idea of using superheated liquid to display the tracks of ionizing particles, just as a cloud chamber utilizes a supersaturated vapor. The instrument based on this concept is known as a Bubble Chamber, because the tracks in bubble chamber consist of a series of closely spaced bubbles. Present video lecture describes Construction & Working along with the Advantages & Limitations of Bubble Detectors.

In 1933, Bainbridge modified the existing mass spectrographs (like Aston’s mass spectrograph, Dempster’s mass spectrometer, etc.) and developed a new spectrograph known as Bainbridge spectrograph. It is based on the principle of velocity selecting/filtering. In this video lecture, we shall learn the Principle of working of spectrometer based on velocity selectors and momentum selector, the construction of spectrometer, mathematical equations involved. It is really interesting to understand how it can resolve 1 amu mass in a fabulous way.