Expectation value.

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 ...

Photoelectric effect.

Photoelectric effect; The emission of electrons by a substance under the action of light is called Photoelectric effect. Photoelectric Effect. Experimental Setup: The phenomenon of photoelectric effect can be studied with the help of an apparatus shown in Figure below. Within an evacuated glass jacket two electrodes R and S are enclosed and the light radiation is allowed to enter the jacket through a quartz window. The radiation falls on electrode R, called cathode. The electrode S can be kept at desired (positive or negative) potential with respect to the cathode. A sensitive ammeter is put in the circuit to record current resulting from photoelectrons. The potential difference between the cathode and anode can be measured by voltmeter . Experimental Setup. Experimental observations The experimental observation of photoelectric effect may be summarised as follows; 1) Effect of Intensity of light on Photoelectric current; For a constant potential difference between the cathode ...

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 fract...

Modern Physics

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