UPSC Physics Atomic Physics Atom and Nucleus

 Atom and Nucleus

1.            Ernst Rutherford (1871-1937)

• British physicist who did pioneering work on radioactive radiation. He discovered alpha-rays and beta-rays.
• Along with Federick Soddy, he created the modem theory of radioactivity. He studied the 'emanation' of thorium and discovered a new noble gas, an isotope of radon, now known as thoron.
• By scattering alpha-rays from the metal foils, he discovered the atomic nucleus and proposed the plenatery lyiodel of the atom. He also estimated the approximate size of the nucleus.

2.            Nucleus    

• In every atom, the positive charge and mass are densely concentrated at the centre of the atom forming its nucleus. The overall dimensions of a nucleus are much smaller than those of an atom.
• Experiments on scattering of \[\alpha \]-particles demonstrated that the radius of a nucleus was smaller than the radius of an atom by a factor of about \[{{10}^{4}}\]. This means the volume ofa nucleus is about \[{{10}^{-12}}\] times the volume of the atom.
• In other words, an atom is almost empty. If an atom is enlarged to the size of a classroom, the nucleus would be of the size of pinhead. Nevertheless, the nucleus contains most (more than \[99.9\]per cent) of the mass of an atom.
• Measurement of atomic masses is carried out with a mass spectrometer, The measurement of atomic masses reveals the existence of different types of atoms of the same element, which exhibit the same chemical properties, but differ in mass. Such atomic species of the same element differing in mass are called isotopes. (In Greek, isotope means the same place, i.e. they occur in the same place in the periodic table of elements). It was found that practically every element consists of a mixture of several isotopes.
• The lightest element, hydrogen has three isotopes. The nucleus of the lightest atom of hydrogen, which has a relative abundance of \[99.98\]per cent, is called the proton.
• The other two isotopes of hydrogen are called deuterium and tritium. Do not occur naturally and are produced artificially in laboratories.
• The positive charge in the nucleus is that of the protons. A proton carries one unit of fundamental charge and is stable. It was earlier thought that the nucleus may contain electrons, but this was ruled out later using arguments based on quantum theory. All the electrons of an atom are outside the nucleus.
• We know that the number of these electrons outside the nucleus of the atom is Z, the atomic number. The total charge of the atomic electrons is thus (-Ze), and since the atom is neutral, the charge of the nucleus is (+Ze). The number of protons in the nucleus of the atom is, therefore, exactly Z, the atomic number.
• Chadwick was awarded the 1935 Nobel Prize in Physics for his discovery of the neutron. A free neutron, unlike a free proton, is unstable. It decays into a proton, an electron and a antineutrino (another elementary panicle), and has a mean life of about 1000 s. It is, however, stable inside the nucleus.
• One also uses the term nucleon for a proton or a neutron. Thus the number of nucleons in an atom is its mass number A.
• The nuclei of isotopes of a given element contain the same number of protons, but differ from each other in their number of neutrons. Chemical properties of elements depend on their electronic structure. As the atoms of isotopes have identical electronic structure they have identical chemical behaviour and are placed in the same location in the periodic table.
• All nuclides with same mass number A are called isobars.

3.           Mass-Energy

• Einstein showed from his theory of special relativity that it is necessary to treat mass as another form of energy. Before the advent of this theory of special relativity it was presumed that mass and energy were conserved separately in a reaction. However, Einstein showed that mass is another form of energy and one can convert mass-energy into other forms of energy, say kinetic energy and vice-versa.
• Einstein gave the famous mass-energy equivalence relation E = mc². Here the energy equivalent of mass m is related by the above equation and c is the velocity of light in vacuum and is approximately equal to \[3\times {{10}^{8}}\] m s^-1.
• Experimental verification of the Einstein's mass-energy relation has been achieved in the study of nuclear reactions amongst nucleons, nuclei, electrons and other more recently discovered particles.
• In a reaction the conservation law of energy states that the initial energy and the final energy are'equal provided the energy associated with mass is also included. This concept is important in understanding nuclear masses and the interaction of nuclei with one another.

4.           Nuclear Binding Energy

• We have seen that the nucleus is made up of neutrons and protons. However oxygen \[{{(}_{8}}{{O}^{16}})\] a nucleus which has 8 neutrons and 8 protons.
• If one wants to break the oxygen nucleus into 8 protons and 8 neutrons, this extra energy \[\Delta M\,\,\,{{c}^{2}}\], has to supplied. This energy required \[{{E}_{b}}\] is related to the mass defect by \[{{E}_{b}}\]\[=\Delta M\,\,\,{{c}^{2}}\]
• If a certain number of neutrons and protons are brought together to form a nucleus of a certain charge and mass, an energy \[{{E}_{b}}\] will be released in the process. The energy \[{{E}_{b}}\] is called the binding energy of the nucleus. If we separate a nucleus into its nucleons, we would have to supply a total energy equal to \[{{E}_{b}}\], to those particles.
• Although we cannot tear apart a nucleus in this way, the nuclear binding energy is still a convenient measure of how well a nucleus is held together. A more useful measure of the binding between the constituents of the nucleus is the binding energy per nucleon.

5.           Nuclear Force

• The force that determines the motion of atomic electrons is the familiar Coulomb force. We have seen that for average mass nuclei the binding energy per nucleon is approximately 8 MeV, which is much larger than the binding energy in atoms. Therefore, to bind a nucleus together there must be a strong attractive force of a totally different kind.
• It must be strong enough to overcome the repulsion between the (positively charged) protons and to bind both protons and neutrons into the tiny nuclear volume.
• The nuclear force is much stronger than the Coulomb force acting between charges or the gravitational forces between masses. The nuclear binding force has to dominate over the Coulomb repulsive force between protons inside the nucleus. This happens only because the nuclear force is much stronger than the coulomb force. The gravitational force is much weaker than even Coulomb force.
• The nuclear force between two nucleons falls rapidly to zero as their distance is more than a few femtometres. This leads to saturation of forces in a medium or a large-sized nucleus, which is the reason for the constancy of the binding energy per nucleon.

6.           Radio Activity

• H. Becquerel discovered radioactivity in 1896 purely by accident. While studying the fluorescence and phosphorescence of compounds irradiated with visible light, Becquerel observed an interesting phenomenon. After illuminating some pieces of uranium- potassium sulphate with visible light, he wrapped them in black paper and separated the package from a photographic plate by a piece of silver. When, after several hours of exposure, the photographic plate was developed, it showed blackening due to something that must have been emitted by the compound and was able to penetrate both black paper and the silver.
• Experiments performed subsequently showed that radioactivity was a nuclear phenomenon in which an unstable nucleus undergoes a decay. This is referred to as radioactive decay. Three types of radioactive decay occur in nature:
• \[\alpha \]-decay in which a helium nucleus ₂He⁴ is emitted;
• \[\beta \]-decay in which electrons or positrons (particles with the same mass as electrons, but with a charge exactly opposite to that of electron) are emitted;
• \[\gamma \]-decay in which high energy (hundreds of keV or more) photons are emitted.
• Different radionuclides differ greatly in their rate of decay. A common way to characterize this feature is through the notion of half-life. Half-life of a radionuclide (denoted by T_1/2) is the time it takes for a sample that has initially.
• Marie Sklodowska Curie (1867-1934) Born in Poland. She is recognised both as a physicist and as a chemist. The discovery of radioactivity by Henri Becquerel in 1896 inspired Marie and her husband Pierre Curie in their researches and analyses which led to the isolation of radium and polonium elements. She was the first person to be awarded two Nobel Prizes-for Physics in 1903 and for Chemistry in 1911.
• Radioactive elements (e.g., tritium, plutonium) which are short-lived i.e., have half-lives much less than the age of the universe (Approx.15 billion years) have obviously decayed long ago and are not found in nature/They can, however, be produced artificially in nuclear reactions.
• There is a release of extra neutron (s) in the fission process. Averagely, \[{{2}^{1/2}}\]neutrons are released per fission of uranium nucleus. It is a fraction since in some fission events 2 neutrons are produced, in some 3, etc. The extra neutrons in turn can initiate fission processes, producing still more neutrons, and so on. This leads to the possibility of a chain reaction. If the chain reaction is controlled suitably, we can get a steady energy output. This is what happens in a nuclear reactor. If the chain reaction is uncontrolled, it leads to explosive energy output, as in a nuclear bomb.
• A very large amount of fissionable material is used for sustaining the chain reaction. What one needs to do is to slow down the fast neutrons by elastic scattering with light nuclei.
• In fact, Chadwick's experiments showed that in an elastic collision with hydrogen the neutron almost comes to rest and proton carries away the energy. This is the same situation as when a marble hits head-on an identical marble at rest.
• Therefore, in reactors, light nuclei called moderators are provided along with the fissionable nuclei for slowing down fast neutrons. The moderators commonly used are water, heavy water (D₂O) and graphite. The Apsara reactor at the Bhabha Atomic Research Centre (BARC), Mumbai, uses water as moderator. The other Indian reactors, which are used for power production, use heavy water as moderator.
• Because of the use of moderator, it is possible that the ratio, K, of number of fission produced by a given generation of neutrons to the number of fission of the preceeding generation may be greater than one. This ratio is called the multiplication factor; it is the measure of the growth rate of the neutrons in the reactor.
• For K = 1, the operation of the reactor is said to be critical, which is what we wish it to be for steady power operation. If K becomes greater than one, the reaction rate and the reactor power increases exponentially. Unless the factor K is brought down very close to unity, the reactor will become supercritical and can even explode. The explosion of the Chernobyl reactor in Ukraine in 1986 is a sad reminder that accidents in a nuclear reactor can be catastrophic.
• The reaction rate is controlled through control-rods made out of neutron-absorbing material such as cadmium. In addition to control rods, reactors are provided with safety rods which, when required, can be inserted into the reactor and K can be reduced rapidly to less than unity.
• The more abundant isotope \[_{92}{{U}^{238}}\] in naturally occurring uranium is non-fissionable. When it captures a neutron, it produces the highly radioactive plutonium through these reactions.
• Plutonium undergoes fission with slow neutrons. The core of the reactor is the site of nuclear fission. It contains the fuel elements in suitably fabricated form. The fuel may be say enriched uranium (i.e., one that has greater abundance of \[_{92}{{U}^{235}}\] than naturally occurring uranium). The core contains a moderator to slow down the neutrons.
• The core is surrounded by a reflector to reduce leakage. The energy (heat) released in fission is continuously removed by a suitable coolant. A containment vessel prevents the escape of radioactive fission products.
• The whole assembly is shielded to check harmful radiation from coming out. The reactor can be shut down by means of rods (made of, for example, cadmium) that have high absorption of neutrons. The coolant transfers heat to a working fluid which in turn may produce stream. The steam drives turbines and generates electricity.
• Like any power reactor, nuclear reactors generate considerable waste products. But nuclear wastes need special care for treatment since they are radioactive and hazardous. Elaborate safety measures, both for reactor operation as well as handling and reprocessing the spent fuel, are required.

7.           Indians Atomic Energy Programme

• The atomic energy programme in India was launched around the time of independence under the leadership of Homi J. Bhabha (1909-1966).
• An early historic achievement was the design and construction of the first nuclear reactor in India (named Apsara) which went critical on 4 August, 1956. It used enriched uranium as fuel and water as moderator.
• Following this was another notable landmark: the construction of CIRUS (Canada India Research U.S.) reactor in 1960. This 40 MW reactor used natural uranium as fuel and heavy water as moderator. Apsara and CIRUS spurred research in a wide range of areas of basic and applied nuclear science.
• An important milestone in the first two decades of the programme was the indigenous design and construction of the plutonium plant at Trombay, which ushered in the technology of fuel reprocessing (separating useful fissile and fertile nuclear materials from the spent fuel of a reactor) in India.
• Research reactors that have been subsequently commissioned include ZERLINA, PURNIMA (I, II and III), DHRUVA and KAMINI. KAMINI is the country's first large research reactor that uses U-233 as fuel. As the name suggests, the primary objective of a research reactor is not generation of power but to provide a facility for research on different aspects of nuclear science and technology. Research reactors are also an excellent source for production of a variety of radioactive isotopes that find application in diverse fields: industry, medicine and agriculture.
• Accordingly, our country has adopted a threestage strategy of nuclear power generation. The first stage involves the use of natural uranium as a fuel, with heavy water as moderator. The Plutonium-239 obtained from reprocessing of the discharged fuel from the reactors then serves as a fuel for the second stage - the fast breeder reactors.
• They are so called because they use fast neutrons for sustaining the chain reaction (hence no moderator is needed) and, besides generating power, also breed more fissile species (plutonium) than they consume.
• The third stage, most significant in the long term, involves using fast breeder reactors to produce fissile Uranium-233 from Thorium-232 and to build power reactors based on them.
• India is currently well into the second stage of the programme and considerable work has also been done on the third - the thorium utilisation - stage. The country has mastered the complex technologies of mineral exploration and mining, fuel fabrication, heavy water production, reactor design, construction and operation, fuel reprocessing, etc. Pressurised Heavy Water Reactors (PHWRs) built at different sites in the country mark the accomplish- ment of the first stage of the programme.
• India is now more than self-sufficient in heavy water production. Elaborate safety measures both in the design and operation of reactors, as also adhering to stringent standards of radiological protection are the hallmark of the Indian Atomic Energy Programme.

8.           Nuclear Fusion - Energy Generation in Stars

• When two light nuclei fuse to form a larger nucleus, energy is released, since the larger nucleus is more tightly bound. We can estimate the temperature at which two protons in a proton gas would (averagely) have enough energy to overcome the coulomb barrier.
• When fusion is achieved by raising the temperature of the system so that particles have enough kinetic energy to overcome the coulomb repulsive behaviour, it is called thermo-nuclear fusion.
• Thermonuclear fusion is the source of energy output in the interior of stars. The interior of the sun has a temperature of \[1.5\times {{10}^{7}}\] K, which is considerably less than the estimated temperature required for fusion of particles of average energy. Clearly, fusion in the sun involves protons whose energies are much above the average energy.
• The fusion reaction in the sun is a multi-step process in which the hydrogen is burned into helium. Thus, the fuel in the sun is the hydrogen in its core.
• Helium is not the only element that can be synthesized in the interior of a star. As the hydrogen in the core gets depleted and becomes helium, the core starts to cool.
• The star begins to collapse under its own gravity which increases the temperature of the core. If this temperature increases to about 108 K, fusion takes place again, this time of helium nuclei into carbon. This kind of process can generate through fusion higher and higher mass number elements.
• The age of the sun is about \[5\times {{10}^{9}}\] y and it is estimated that there is enough hydrogen in the sun to keep it going for another 5 billion years. After that, the hydrogen burning will stop and the sun will begin to cool and will start to collapse under gravity, which will raise the core temperature. The outer envelope of the sun will expand, turning it into the so called red giant.

9.           Nuclear Holocaust

• In a single uranium fission about \[0.9\times 235\] MeV (\[\approx \,200\] MeV) of energy is liberated. If each nucleus of about 50 kg of \[^{235}U\] undergoes fission the amount of energy involved is about \[4\times {{10}^{15}}\]J. This energy is equivalent to about 20,000 tons of TNT, enough for a superexplosion.
• Uncontrolled release of large nuclear energy is called an atomic explosion.
• On 6 August, 1945 an atomic device was used in warfare for the first time. The US dropped an atom bomb on Hiroshima, Japan. The explosion was equivalent to 20,000 tons of TNT. Instantly the radioactive products devastated 10 sq.km of the city which had 3,43,000 inhabitants. Of this number 66,000 were killed and 69,000 were injured; more than 67 per cent of the city's structures were destroyed.
• High temperature conditions for fusion reactions can be created by exploding a fission bomb. Super-explosions equivalent to 10 megatons of explosive power of TNT were tested in 1954. Such bombs which involve fusion of isotopes of hydrogen, deuterium and tritium are called hydrogen bombs.
• It is estimated that a nuclear arsenal sufficient to destroy every form of life on this planet several times over is in position to be triggered by the press of a button. Such a nuclear holocaust will not only destroy the life that exists now but its radioactive fallout will make this planet unfit for life for all times.
• Scenarios based on theoretical calculations predict a long nuclear winter, as the radioactive waste will hang like a cloud in the earth's atmosphere and will absorb the sun's radiation.

10.        Important Facts

• The density of nuclear matter is independent of the size of the nucleus. The mass density of the atom does not follow this rule.
• Radioactivity is an indication of the instability of nuclei. Stability requires the ratio of neutron to proton to be around \[1:1\] for light nuclei. This ratio increases to about \[3:2\] for heavy nuclei. (More neutrons are required to overcome the effect of repulsion among the protons.)
• Nuclei which are away from the stability ratio, i.e., nuclei which have an excess of neutrons or protons are unstable. In fact, only about 10 per cent of knon isotopes (of all elements), are stable. Others have been either artificially produced in the laboratory by bombarding a, p, d, n or other particles on targets of stable nuclear species or identified in astronomical observations of matter in the universe.