Question

Iron-56 has one of the highest binding energies of all nuclides. Calculate its nuclear binding energy in
kJ per mol nucleon. 1 amu is equivalent to 1.492 ´ 10^-10 J.

mass of iron-56 nuclide	55.934994 amu (includes electrons)
proton mass	1.00728 amu
neutron mass	1.00866 amu
electron mass	5.4858 ´ 10–4 amu
speed of light	2.998 ´ 108 m/s

Answer 1

Solution

Lets first calculate the mass difference (mass deffect)

Atomic nubmer of iron is 26 and mass number is 56 thereofre it conatins 26 protons and 30 neutrons

so mass of protons = 26 * 1.00728 amu = 26.18928 amu

mass of neutrons = 30 * 1.00866 amu = 30.2598 amu

mass deffect = (mass of proton + mass of neutron) - atomic mass

                    = (26.18928 amu+30.2598 amu) - 55.934994 amu

                   = 0.514086 amu

Now lets calculate the binding energy by using the following formula

Binding energy = mass deffect * 9.31 MeV per amu

                      = 0.514086 amu * 9.31 MeV per amu

                      = 4.786 MeV

now lets convert this energy from MeV to Joules

1 MeV= 1.60217657 *10^-13 J

4.786 MeV * 1.60217657 *10^-13 J / 1 MeV = 7.668*10^-13 J

now lets convert this energy per nucleon

7.668*10^-13 J / 56 nucleon = 1.3693 *10^-14 J/nucleon

now convert this to per mole of nucleon

1.3693 *10^-14 J/nucleon * 6.022*1023 nucleon = 8.25*10⁹ J / mol nucleon

now lets convert joules into kJ

8.25*10⁹ J / mol nucleon * 1 kJ / 1000 J

= 8.25*10⁶ KJ / mol nucleon