Nuclear Mass, Binding Energy, Mass defect Of Atomic Nucleus

nuclear mass is the mass of the  nucleus of an atom, the mass of   the nucleons combined is the nuclei mass, the sum of the protons and the neutrons will give the nuclear/atomic  mass of each and every atom, the mass of the electrons are negligible because they are 1840 time less than the nucleon mass therefore they did not add any value to atomic masses, this is why nuclear and atomic masses have same value.

 there are two type of nuclear mass , the calculated mass and the actual or measured mass, the  calculated mass is the value obtain when the sum  of protons and neutrons in an atom are taken, if a given atom has N_n as number of neutrons and P_n as number of protons, then the atomic mass will be

Atomic mass = number of protons + number of neutrons,  Z =P_n + N_n. This is he calculated mass.

 the measured mass also called the actual mass, is the mass obtained when a  atom or nuclei mass is measured with a mass spectrometer, it is also called the actual mass. This mass is found to be less than the calculated mass, the sum of the nucleons  is found to be less than the  measured atomic mass, why the discrepancy? Where does the mass go? According to nuclear theory the lost mass is said to be converted into force for keeping the protons and neutrons together in the nucleus of the atom, it is called the inter-nucleon force. If this force is absent the positively charged protons will fly apart due to the repulsive coulomb force between them. The difference between the calculated mass and the measured mass is called mass defect. The energy release released when the nucleons combined to form the nucleus is called binding energy. It is the energy required to bring a given number of protons and neutron to form a nucleus. Or the energy release when a nucleus is split into its constituent protons and neutrons.  Below is a table of some nuclei, with calculated mass, actual mass and the discrepancies between the two masses , the binding energy of each nucleus can be obtained by multiplying the mass defects with c².

Nuclei	Calculated mass	Measured mass	Mass defects
Helium	4.03298	4.0026	0.03038
Silicon	28.23086	28.0855	0.14536
Beryllium	9.074625	9.0122	0.052625
Boron	10.8245	10.811	0.0135
Nitrogen	14.11543	14.0067	0.10873

Albert Einstein observed this mass defects and argue that lost mass is due to the energy release when the nucleus of an atom is formed, according to Einstein mass and energy are interchangeable,  the lost mass is converted into energy and the einstein put the ratio with his famous mass-energy relation  given by E =∆mc². Where  E is energy, ∆ mass loss, c²  is the speed of light squared in the order of  300,000,000m/s,  with this relation it means that an enormous  amount of energy will be released when small mass is loss and large tremendous  of energy is required to destroy a small mass. This is the basis where nuclear energy and weapon are built.

converting 1kg mass to  to energy,

1 * (3*10²)= 9*10¹⁶

1Ev =1.6*10^-19

 1u = {1.66* 10^-27 * 9*10¹⁶ }/1.6*10^-19

=931.5 MeV

CALCULATING THE BINDING ENERGY OF NUCLEI

P_n * Mass of proton + N_p * Mass of neutrons = calculated mass

P_n * 1.007825 + N_P * 1.008665 = ACTUAL MASS

mass defect = calculated mass – actual mass

 binding energy = mass defect * C²

∆E =∆MC²