Nuclear Mass Defect | Nuclear Binding Energy

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What is Nuclear Mass Defect?

What is Nuclear Binding Energy?

Answer:

Mass Defect: we know the total number of protons and neutrons as nucleons. They composed the difference between the mass of a nucleus and the sum of the masses of the nucleons of which is called the mass defect. When the nucleus formed by nucleons then it is, find that the expected mass of a nucleus is greater than the sum of the masses of the nucleons. We know the difference of the masses as Mass Defect.

Mass Defect = [Number of Protons X Mass of a proton + Number of Neutron

X Mass of Neutron] – Actual mass of Nucleus

The symbolization of an atom is represented as   than

Mass Defect =>  Δm = [Z X m_p+ (A-Z) m_n]-M

 

where: Δm=mass defect (amu); M = Actual mass of Nucleus (Atomic Mass) m_p=mass of a proton   (1.007277 amu); m_n=mass of a neutron (1.008665 amu); m_e=mass of an electron   (0.000548597 amu)

Particle	Mass (kg)	Mass (u)	Mass (Mev/c2)
1 atomic mass unit	1.660540 x 10-27 kg	1.000 u	931.5 MeV/c2
neutron	1.674929 x 10-27 kg	1.008664 u	939.57 MeV/c2
proton	1.672623 x 10-27 kg	1.007276 u	938.28 MeV/c2
electron	9.109390 x 10-31 kg	0.00054858 u	0.511 MeV/c2

For carbon-12 atom as   :

The carbon-12 atom has a mass of 12.000 u, and yet it contains 12 objects (6 protons and 6 neutrons) that each has a mass greater than 1.000 u:

 

Mass defect => Δm = 6 X 1.008664 u + 6 X 1.007276 u + 6 X 0.00054858 u – 12.000 u = 0.098931 u

The binding energy in the carbon-12 atom is therefore 0.098931 u X 931.5 MeV/u = 92.15 MeV.

Once the mass defect is known, nuclear binding energy can be calculated by converting that mass to energy by using E=mC².

Binding Energy: The Nuclear binding energy is equal to the energy liberated when the nucleus is formed from other nuclei. All nuclei have some binding energy, which depends upon the number of nucleons of the nucleus. If the mass number is 20<A<200; then per nucleon binding energy is ~8.0 Mev, and these types of a nucleus are in a stable state. For those nuclei having A>200; then per nucleon binding energy is about ~7.6 Mev and the nucleus is unstable.

Binding Energy B = (Δm).C²

B = [{Z X m_p+ (A-Z) m_n}-M]. C²

The nuclear binding energy may also refer to the energy balance in processes in which the nucleus splits into fragments composed of over one nucleon. If new binding energy is available when light nuclei fuse, or when heavy nuclei split, either process can cause the release of this binding energy. When a large nucleus splits into pieces, it emitted excess energy as photons (gamma rays) and as the kinetic energy of several ejected particles (nuclear fission products). The nuclear binding energies and forces are on the order of a million times greater than the electron binding energies of light atoms like hydrogen. The mass defect of a nucleus represents the mass of the energy of binding of the nucleus and is the difference between the mass of a nucleus and the sum of the masses of the nucleons of which it is composed.

For the alpha particle Δm= 0.0304 u which gives binding energy of 28.3 MeV.