Question

Calculate the nuclear binding energy (in J) and the binding energy per nucleon for the following isotope:

₅₃¹²⁷ I (126.9004 amu)

Nuclear binding energy = __________ x 10 ^__________ J

Binding energy per nucleon = _________ x 10 ^_________ J/nucleon

Answer 1

Mass defect , ?m = ( ZM_H + (A-Z) M _n ) - M

Where

Z = atomic number of I = 53

(A-Z) = No. of neutrons = 127-53 = 74

M_H = mass of Hydrogen atom = 1.007825 amu

M _n = mass of Neutron = 1.008665 amu

M = real mass = 126.9004 amu

Plug the values we get ?m = [( 53x1.007825)+ (74x1.008665 )] - 126.9004

                                        = 1.155535 amu

So nuclear binding energy , BE = ?m x 931.5 MeV

                                             = 1.155535 x931.5 MeV

                                               = 1076.38 MeV

                                               = 1076.38 x 10⁹ eV

                                               = 1076.38 x 10⁹ x 1.6x10^-19 J

                                               = 1722.2 x 10^-10 J

Binding energy per nucleon = BE / atomic mass number

                                        = 1722.2 x 10^-10 / 127 J / necleon

                                       = 1.3561 10 ^-9 J/nucleon