Summary

An atom has a nucleus. The nucleus is positively charged. The radius of the nucleus is smaller than the radius of an atom by a factor of $10^{4}$ . More than 99.9% mass of the atom is concentrated in the nucleus.
On the atomic scale, mass is measured in atomic mass units (u). By definition, 1 atomic mass unit $(1 u)$ is $1 / 12^{th}$ mass of one atom of $^{12}$ C; $1 u = 1.660563 \times 10^{- 27} kg$
A nucleus contains a neutral particle called neutron. Its mass is almost the same as that of proton
The atomic number Z is the number of protons in the atomic nucleus of an element. The mass number A is the total number of protons and neutrons in the atomic nucleus; A = Z+N; Here N denotes the number of neutrons in the nucleus.
A nuclear species or a nuclide is represented as $z^{A} X$ , where $X$ is the chemical symbol of the species.
Nuclides with the same atomic number Z, but different neutron number N are called isotopes. Nuclides with the same A are isobars and those with the same N are isotones.
Most elements are mixtures of two or more isotopes. The atomic mass of an element is a weighted average of the masses of its isotopes and calculated in accordance to the relative abundances of the isotopes.
A nucleus can be considered to be spherical in shape and assigned a radius. Electron scattering experiments allow determination of the nuclear radius; it is found that radii of nuclei fit the formula $R = R_{0} A^{1 / 3}$ where $R_{0} =$ a constant $= 1.2 fm .$ This implies that the nuclear density is independent of $A$ . It is of the order of $10^{17} kg / m^{3}$ .
Neutrons and protons are bound in a nucleus by the short-range strong nuclear force. The nuclear force does not distinguish between neutron and proton.
The nuclear mass $M$ is always less than the total mass, $Σ m,$ of its constituents. The difference in mass of a nucleus and its constituents is called the mass defect. $Δ M = (Z m_{p} + (A - Z) m_{n}) - M$ Using Einstein's mass energy relation, we express this mass difference in terms of energy as $Δ E_{b} = Δ M c^{2}$ The energy $Δ E_{b}$ represents the binding energy of the nucleus. In the mass number range $A = 30$ to $170,$ the binding energy per nucleon is nearly constant, about $8 MeV /$ nucleon.
Energies associated with nuclear processes are about a million times larger than chemical process.
The Q-value of a nuclear process is Q = final kinetic energy – initial kinetic energy. Due to conservation of mass-energy, this is also, $Q = (sum of initial masses - sum of final masses) c^{2}$
Radioactivity is the phenomenon in which nuclei of a given species transform by giving out $α$ or $β$ or $γ$ rays; $α$ -rays are helium nuclei; $β$ -rays are electrons. $γ$ rays are electromagnetic radiation of wavelengths shorter than X-rays;
Law of radioactive decay : $N (t) = N (0) e^{- λ t}$ where $λ$ is the decay constant or disintegration constant. The half-life $T_{1 / 2}$ of a radionuclide is the time in which $N$ has been reduced to one-half of its initial value. The mean life $τ$ is the time at which $N$ has been reduced to $e^{- 1}$ of its initial value $T_{1 / 2} = \frac{\ln 2}{λ} = τ \ln 2$
Energy is released when less tightly bound nuclei are transmuted into more tightly bound nuclei. In fission, a heavy nucleus like 235 92 U breaks into two smaller fragments, $e . g .,_{92}^{235} U +_{0}^{1} n \to_{51}^{133} Sb +_{41}^{99} Nb + 4_{0}^{1} n$
The fact that more neutrons are produced in fission than are consumed gives the possibility of a chain reaction with each neutron that is produced triggering another fission. The chain reaction is uncontrolled and rapid in a nuclear bomb explosion. It is controlled and steady in a nuclear reactor. In a reactor, the value of the neutron multiplication factor k is maintained at 1.
In fusion, lighter nuclei combine to form a larger nucleus. Fusion of hydrogen nuclei into helium nuclei is the source of energy of all stars including our sun.