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 \(1 / 12^{\text {th }}\) mass of one atom of \({ }^{12}\) C; \(1 \mathrm{u}=1.660563 \times 10^{-27} \mathrm{~kg}\)
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 \(=1.2 \mathrm{fm} .\) This implies that the nuclear density is independent of \(A\). It is of the order of \(10^{17} \mathrm{~kg} / \mathrm{m}^{3}\).
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, \(\Sigma m,\) of its constituents. The difference in mass of a nucleus and its constituents is called the mass defect. \(\Delta M=\left(Z m_{p}+(A-Z) m_{n}\right)-M\) Using Einstein's mass energy relation, we express this mass difference in terms of energy as \(\Delta E_{b}=\Delta M c^{2}\) The energy \(\Delta E_{b}\) 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 \(8 \mathrm{MeV} /\) 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, \[ Q=(\text { sum of initial masses }-\text { sum of final masses }) c^{2} \]
Radioactivity is the phenomenon in which nuclei of a given species transform by giving out \(\alpha\) or \(\beta\) or \(\gamma\) rays; \(\alpha\) -rays are helium nuclei; \(\beta\) -rays are electrons. \(\gamma\) rays are electromagnetic radiation of wavelengths shorter than X-rays;
Law of radioactive decay : \(N(t)=N(0) \mathrm{e}^{-\lambda t}\) where \(\lambda\) 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 \(\tau\) is the time at which \(N\) has been reduced to \(e^{-1}\) of its initial value \(T_{1 / 2}=\frac{\ln 2}{\lambda}=\tau \ln 2\)
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, \(\mathrm{e} . \mathrm{g} .,{ }_{92}^{235} \mathrm{U}+{ }_{0}^{1} \mathrm{n} \rightarrow{ }_{51}^{133} \mathrm{Sb}+{ }_{41}^{99} \mathrm{Nb}+4_{0}^{1} \mathrm{n}\)
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.