Explain mass defect and binding energy with example.

1.	Explain mass defect and binding energy with example.
Answer» The nuclear mass M is always less than the total mass of its constituents. The difference in mass of a nucleus and its constituents ΔM is called the mass defect, ΔM = (Z m_p + (A – Z)m_n) – M Using Einstein’s mass energy relation, we express this mass difference in terms of energy as ΔE_b = ΔM c² The energy ΔE_b represents the binding energy of the nucleus. In the mass number range A = 30 to 170, the binding energy per nucleon is nearly constant, about 8 MeV/nucleon. Example : The atomic mass of nucleus of ¹⁶₈O found from mass spectroscopy experiments is seen to be 15.99053 u. The expected mass of ¹⁶₈O nucleus is by adding 8 protons mass and 8 neutrons mass = 16.12744 u. The difference between these two masses is mass defect = 0.13691 u.

Answer»

The nuclear mass M is always less than the total mass of its constituents. The difference in mass of a nucleus and its constituents ΔM is called the mass defect,

ΔM = (Z m_p + (A – Z)m_n) – M

Using Einstein’s mass energy relation, we express this mass difference in terms of energy as

ΔE_b = ΔM c²

The energy ΔE_b represents the binding energy of the nucleus. In the mass number range A = 30 to 170, the binding energy per nucleon is nearly constant, about 8 MeV/nucleon.

Example :

The atomic mass of nucleus of ¹⁶₈O found from mass spectroscopy experiments is seen to be 15.99053 u. The expected mass of ¹⁶₈O nucleus is by adding 8 protons mass and 8 neutrons mass = 16.12744 u.

The difference between these two masses is mass defect = 0.13691 u.

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