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BASIC PROPERTIES OF NUCLEUS:anit jentist, 1. Size of the Nucleus: The size of the Nucleus was determined by Se —_, isi roximately, Rutherford with a- scattering experiment. The value of this is approx, , as 10° m, , 5 : roportional |, The volume of the nucleus of radius R is approximately propor 0 the, , p ‘ . hen, total number of the constituent particles i.e. the mass number A. T, , VaA, 43nRaA, RaA, R=RoA, R=R A?, , Where Ro is proportional constant. Ro = 1.3 X 10° mor 13 Fermi., , 2. Charge of the Nucleus: Nucleus consists of Kiftors and neutrons. Neutrons are, , neutral charge. So the charge of the riucleus iho the protons. Each proton has a, positive charge equal in magnitude. to that of an electron. It can be measured, basing on scattering of a- patticles or by studying characteristic x-ray spectrum,, , The charge of the nucleus is +Ze: Charge of proton is +1.6 x 10° mG,, , 3. Mass of the Nucleus: Total mass of the constituent nucleons present in the, nucleus is called as mass of the nucleus. The unit of mass of the nucleus is a.m.u. |, am.u = 1.66 x 10?’ kg. The mass of the nucleus is measured with mass, spectrometer. Vormu = 13S MEV,, , Ce, If poe the mass of proton, m, is the mass of neutron and Xisthe, , , , , x ee, , z comic ateenenembecoi ota Srethe-ato, they Mass of the Nucleus = Z m, en ge, > The difference in between total mass of the constituent nucleons and real mass 0!, the nucleus is called as Mass Defect. It is denoted by Am., Mass defect (Am ) = { Zm, +N m,} -M, > The Mass defect per nucleon is called Packing fraction ‘f’, Packing fraction (f) = Am/A.

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3, 4. Spin of the Nucleus: Like electron, the nucleus also having a spin [7 e fine, , structure of spectral lines in atomic spectra was explained on the basis of lectron, spin. Many of these fine structure limes show still fine structure called Hy erfine, structure which has been attributed to nuclear spin} It is denoted by ‘I’., , The proton and neutrons each have spin angular momentum, like, clectron. Ineadidtitton the nucleons also posses quantized orbital angular, momentum about the centre of mass of the nucleus like electron in the, atom. So, the total spin of the nucleus is the addition of vector sum of, , orbital angular momentum (L) and spin angular momentum (S) of the, , nucleons,, I=L+8, 5. Magnetic dipole moment of Nuclei (1):, , The spinning electron is associated with a magnetic dipole moment i.e., , ftp =e(h/2n) =ech, , 2m 2m,, Here, pip is called Bhor magneton., , According to Dirac’s theory the proton also associated with magnetic dipole, , moment like electron., , fy =e(h/2n) =ch, 2m, 2m,, Where pty is called Nuclear magneton. It is unit of magnetic moment., , The nuclear magneton is 1/1836 of a Bhor magneton. The magnetic moments of, nucleus are found to vary in between -2 to +4., 6. Electric quadrupole moment (Q):, , The distortion of the shape of a nucleus from sphere is measured by a quantity, called its electric quadrupole moment. It is denoted by ‘Q’. The electric quadrupole, , moment is measured by using the following equation., , Q=2Ze(b’-a), 5, , , , iF

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th? 7 i 1 4, Where ‘a’ is radius along the axis of symmetry and ‘b’ is the radius in th,, , perpendicular direction., Depending upon the electric quadrupole moment values the shape of the nucleys, , having the below shapes., , a, , , , Q=0 Q=-ve Q=tve, , Spherical shape Oblate spheroid prolate spheroid ’, a=b a>b a<b \, , 7. Binding Energy (B.E):, , The minimum energy required to separate a stable “nucleus into its constituent, protons and neutrons is called “Binding Energy”., (OR), The energy which is equivalence to mass defect is also called Binding Energy of, , the Nucleus., , BE =(Zm, + Nm) - Mm |c, Where ‘m,’ and ‘mj are masses of the proton and the neutron respectively. ‘M’ is, , the mass of the nucleus. Here {(Zm, + Nm,) — M} is called Mass defect., , , , Where ‘M’ is the difference in measured mass and ‘A’ is the mass number, Note : Binding energy is also defined as the energy required to decompose a nucleus into, its constituent particles. ‘, Average Binding Energy: The ratio between Binding energy and atomic mass numbel, , is called avg. Binding energy per nucleon or Packing fraction., , The graph is drawn between atomic mass number (A) and average Binding Ener), , per nucleon. The shape of the graph is like as shown in figure., , =, , ==