Question

One atom of 202Hg has a mass of 201.970 644 amu. Calculate the nuclear binding energy per atom and per nucleon of this nuclide. Note: The atomic mass includes the mass of the electrons also. The mass of a proton is 1.0072765 amu, the mass of a neutron is 1.0086649 amu and the mass of an electron is 0.0005486 amu.

Answer 1

Nuclear Binding Energy (N.B.E) is the energy to seperate a nuclues into its constituent protons and neutrons or amount of energy liberated. To calculate Nuclear Binding Energy (N.B.E) we have the given expression as given below :

Nuclear Binding Energy (N.B.E) = ∆m x 931 MeV

where ∆m = mass defect which is the amount of loss of mass in the construction of the atom ∆m = (A-Z) m_n + Zm_p + Zm_e - M

A = calculated atomic mass = 202 amu

Z = atomic number = 80

m_n = mass of a neutron = 1.0086649 amu

m_p = mass of a proton = 1.0072765 amu

m_e = mass of an electron = 0.0005486 amu

M = measured atomic mass =  201.970 644 amu

∆m = (202 - 80)*1.0086649 amu + 80*1.0072765 amu + 80*0.0005486 amu - 201.970 644 amu

∆m = 203. 6831258 amu - 201.970 644 amu

∆m = 1.7124818 amu

∴ Nuclear Binding Energy (N.B.E) per atom = 1.7124818 x 931 MeV =1594 .32 MeV

and Nuclear Binding Energy (N.B.E) per nucleon , B = (N.B.E) / A = 1594 .32 MeV / 202 = 7.89 MeV

Nuclear Binding Energy (N.B.E) per nucleon is the property which measures the stability of a nucleus