Nuclear charge, Nuclear mass,Nuclear density and nuclear size.

Nuclear charge;

The nucleus consist of protons and neutrons. Since neutrons do not have any charge, thus the nuclear charge is equal to the integral multiple of proton charge i.e Ze where Z is the number of protons inside the nucleus.

In 1914, Mosley determined the nuclear charge during the study of wavelength of X-ray emitted from different elements. Since the atom is electrically neutral, it can be explained that atomic number X represents the number of electrons outside the nucleus and is equal to number of protons inside the nucleus and the sum of number of protons and neutrons inside the nucleus is called mass number A. Thus the number of neutrons inside the nucleus i.e N=A-Z.

Nuclear mass;

Almost the entire mass of an atom (~99.75%) is concentrated in the nucleus. Nuclear mass is obtained by subtracting electrons mass from atomic mass. Nuclear mass is not exactly equal to the integral multiple of standard atomic mass unit except ¹²C₆. But the nuclear mass is nearly equal to the integral multiple of the unit.

Nuclear density;

The density of the nucleus is very high as the size of the nucleus is very small.

Nuclear density.

Thus nuclear density is independent of mass number A. The nuclear density of all nuclei are same.

Nuclear Size;

The shape of the nucleus is taken spherical, because for a given volume this shape possesses the least surface area. The radius of a nucleus of a mass number A is directly proportional to A^1/3.

Nuclear Size.

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Mass defect, packing fraction and binding energy.

Mass defect, packing fraction and binding energy: It was assumed that mass of the nucleus is equal to the mass of its constituents (i.e protons and neutrons). But experimentally it was found that the actual mass of the nucleus is less than the theoretical mass. Thus, the difference between the theoretical mass and experimental mass is called mass defect i.e ∆m={[Zmₚ + (A-Z)mₙ] - M} Where mₚ= mass of proton mₙ= mass of neutron M= actual mass of nucleus Z= atomic number A= mass number The ratio of mass defect and mass number (A) is called packing fraction (f) f = ∆m/A Thus packing fraction is the mass defect available per nucleon. The packing fraction explains the stability of the nucleus. The packing fraction may be positive, negative or zero. The positive value of packing fraction indicates that the nuclei is unstable while the negative value of packing fraction indicates that a fraction of nucleus mass has been converted into e

LS coupling and jj coupling.

Total angular momentum: The total angular momentum of an electron is the sum of the orbital angular momentum and spin angular momentum of the electron i.e Coupling Scheme Since an atom consist of large number of electrons having different orbital and spin momenta, Coupling scheme is necessary to obtain the resultant orbit and spin momenta of atom as a whole. There are two types of coupling scheme namely 1) LS Coupling 2) JJ Coupling. 1)LS Coupling: In this coupling the 'l' vectors of all electrons combine to form resultant 'L' vector and all the 's' vectors of these electrons combine to form resultant 'S' vector. Then the 'L' vector and 'S' vector undergoes vector addition to give resultant 'J' vector which represents the total angular momentum of an atom. Symbolically LS coupling is represented as This type of coupling is governed by the following principles: 1) All the three vectors (L,S and J vectors) are quantized. 2)L is an

Different kinds of beta decay.

Different kinds of beta decay 1) Negative beta decay process: When there is excess number of neutrons in the nucleus, the neutron is converted into proton with the emission of electron and antineutrino particle and this process is called negative beta decay process. Negative beta decay. 2) Positive beta decay process: When there is excess number of protons in the nucleus, the proton is converted into neutron with the emission of positron and neutrino particle and this process is called positive beta decay process. Positive beta decay. 3) Electron Capture: When there is excess number of protons in the nucleus, sometimes the nucleus will absorbed the nearby electrons in the nearest electron orbital emitting neutron and a neutrino and this process is called electron capture. Electron capture. 4) Inverse beta decay: Inverse beta decay. Thus such kind of reaction in which neutrinos are absorbed to create some sort of beta decay is called inverse beta decay. Inverse beta decay confirm the e

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