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JEE Main and JEE Advanced Syllabus of Modern Physics

Modern Physics is a very important constituent of Physics portion of the IIT JEE. It is interesting as well as usually fetches many questions in the JEE. It includes topics like Nuclear Fission and Fusion which are easy to master. These topics are quite fascinating but involve concepts which must be understood properly.
Modern Physics for IIT JEE refers to the Physics based on the two major branches: relativity and quantum mechanics. Classical Physics refers to the traditional Physics which was based on the concepts before coming up of Modern Physics. There were various theoretical and experimental paradoxes that forced thinking out of the traditional path. Modern physics is generally encountered when dealing with extreme conditions. Quantum mechanical effects appear in circumstances dealing with "lows" (low temperatures, small distances), while relativistic effects tend to appear when dealing with "highs" (high velocities, large distances), the "middles" being classical behavior. The Classical Physics was indeed in accord with common sense. Modern Physics has in fact come over that and imparts a better understanding of nature. Modern Physics in IIT JEE syllabus is the most scoring part.
Nuclear Fission and Fusion: Nuclear Fission and Fusion are two different kinds of energy releasing reactions. In these reactions, the energy is released from high- powered atomic bonds between the particles present in the nucleus. The two processes are quite opposite in nature. While Fission involves the splitting of an atom into two or more atoms, in Fusion, two or more smaller atoms combine to form a larger atom. We discuss both the processes one by one.

Nuclear Fission:Nuclear Fission is the process of splitting atoms. It is a process in nuclear physics in which the nucleus of the atom into smaller nuclei as fission products along with some by-produce particles. Fission hence may be termed as a form of elemental transmutation.

The by-products comprise free neutrons and photons which are generally in the form of gamma rays in addition to other nuclear fragments such as beta particles and alpha particles. Fission is an exothermic reaction which means there is a release of huge amount of energy when it takes place. Fission of heavy elements releases considerable amount of useful energy either in the form of gamma rays or as kinetic energy of the fragments. This energy may be used for nuclear power or for the explosion of nuclear weapons.

The sum of the masses of these fragments is less than the original mass. This gap  in  the mass which is around 0.1 percent of the original total mass has been  converted  into energy according to Einstein's equation.
Nuclear Fusion: In simple words, Fission refers to the process in which two or more atoms combine to form a larger atom. Nuclear energy can also be released by fusion of two light elements (elements with low atomic numbers). The power that fuels the sun and the stars is nuclear fusion. In a hydrogen bomb, two isotopes of hydrogen, deuterium and tritium are fused to form a nucleus of helium and a neutron. It may also be defined as the process in which multiple nuclei join together to form a heavier nucleus. It is accompanied by the release or absorption of energy depending on the masses of the nuclei involved.

Radioactive Decay of Substances
Radioactive decay, as the word suggests refers to the decay to attain stability. It refers to the loss of particles from an unstable atom in order to attain more stability. The unstable elements emit some particles from their nucleus to gain stability and this process is termed as radio-activity. For elements, uniformity is produced by having an equal number of neutrons and protons which determines and henceforth directs the nuclear forces to keep the nuclear particles inside the nucleus. There may be cases when a particle becomes more frequent than another and hence creates an unstable nucleus. The unstable nucleus then releases radiation in order to gain stability.
This radio-active decay can occur in five forms:
1.) Alpha emission
2.) Beta emission
3.) Positron emission
4.) Electron capture
5.) Gamma emission

As stated above, each decay emits some specific particle which also changes the type of product produces. The nuclei produced from the decay are called the daughter nuclei. The type of decay also determines the number of neutrons and protons found in the daughter nuclei. Let us consider an example of a radioactive substance.
The stable Beryllium contains 4 protons and 5 neutrons in its nucleus. A lighter isotope of beryllium is also available which contains 4 protons and only 3 neutrons, which gives a total mass of 7 amu. This isotope decays into Lithium-7 through electron capture. A proton from Beryllium-7 captures a single electron and becomes a neutron. This reaction produces a new isotope (Lithium-7) that has the same atomic mass unit as Beryllium-7 but one less proton which stabilizes the element. 

Beta decay occurs when the neutron to proton ratio is too great in the nucleus and causes instability. In basic beta decay, a neutron is turned into a proton and an electron. The electron is then emitted. Here's a diagram of beta decay with hydrogen-3:

Half-Life is a very common term associated with radio-active decay. It cannot be easily detected when a single radioactive atom will decay. But, we can get an idea about the time required for half a large number of identical radioactive atoms to decay. This time is called the half-life.

Structure of Atom and Nucleus:
An atom is made up of three subatomic particles: protons, neutrons and electrons. The protons and neutrons are placed inside the nucleus. The nucleus is at the center of the atom. The electrons keep on moving in orbits around the nucleus. The nature of the atom is determined by the number of protons. The protons carry positive charge, while electrons are negatively charged. Neutrons, as the name suggests are neutral and do not carry any charge. If the nucleus contains 17 protons, then the atom is chlorine. An atom of oxygen contains 8 protons in its nucleus.

The nucleus is the dense central core of the atom which contains both the protons as well as the neutrons. Electrons are outside the nucleus in energy levels. Protons have a positive charge, neutrons have no charge, and electrons have a negative charge. An atom is said to be neutral of it has the same number of protons and electrons. The neutrons can vary in number in the atom of a particular element. Atoms of the same element that have differing numbers of neutrons are called isotopes.

The formula for finding the atomic number of an elemnet is given by
Atomic Number = Number of electrons – Number of Protons