Nuclear Binding Energy
The energy required to break down a nucleus into its component nucleons
is called the nuclear binding energy.
63Cu + Energy 29 p+ + 34 no
Nuclear binding energies are usually expressed in terms
of kJ/mole of nuclei or MeV's/nucleon. Calculation of the nuclear binding
energy involves the following three steps:
the Mass Defect
The difference between the mass of a nucleus and the sum
of the masses of the nucleons of which it is composed is called the mass
defect. Three things need to be known in order to calculate the mass defect:
To calculate the mass defect:
the actual mass of the nucleus,
the composition of the nucleus (number of protons and
the masses of a proton and of a neutron.
Example: Find the mass defect of a copper-63 nucleus if the
actual mass of a copper-63 nucleus is 62.91367 amu.
add up the masses of each proton and of each neutron
that make up the nucleus,
subtract the actual mass of the nucleus from the combined mass
of the components to obtain the mass defect.
Find the composition of the copper-63 nucleus and determine the
combined mass of its components.
Copper has 29 protons and copper-63 also has (63 - 29) 34 neutrons.
29 protons(1.00728 amu/proton) + 34 neutrons(1.00867 amu/neutron)
mass of a proton is 1.00728 amu and a neutron is 1.00867 amu.
combined mass is calculated:
Calculate the mass defect.
Dm = 63.50590 amu - 62.91367 amu =
of Mass Defect into Energy
To convert the mass defect into energy:
Example: Determine the binding energy of the copper-63 atom.
Convert the mass defect into kilograms (1 amu =
1.6606 x 10-27 kg)
Convert the mass defect into its energy equivalent using Einstein's
(0.59223 amu/nucleus)(1.6606 x 10-27 kg/amu) = 9.8346
x 10-28 kg/nucleus
Convert the mass defect (calculated in the previous example) into
E = (9.8346 x 10-28 kg/nucleus)(2.9979 x 108
m/s)2 = 8.8387 x 10-11 J/nucleus
Convert this mass into energy using DE
= Dmc2, where c = 2.9979 x 108
Nuclear Binding Energy as Energy per Mole of Atoms, or as Energy per Nucleon
The energy calculated in the previous example is the nuclear binding
energy. However, nuclear binding energy is often expressed
as kJ/mol of nuclei or as MeV/nucleon.
(8.8387 x 10-11 J/nucleus)(1 kJ/1000 J)(6.022 x 1023
nuclei/mol) = 5.3227 x 1010 kJ/mol of nuclei
To convert the energy to kJ/mol of nuclei we will simply employ the conversion factors for
converting joules into kilojoules (1 kJ = 1000 J) and for converting
individual particles into moles of particles (Avogadro's Number).
(8.8387 x 10-11 J/nucleus)[1 MeV/(1.602 x 10-13
J)](1 nucleus/63 nucleons) = 8.758 MeV/nucleon
To convert the binding energy to MeV (megaelectron volts) per nucleon
we will employ the conversion factor for converting joules into MeV (1
MeV = 1.602 x 10-13 J) and the number of nucleons (protons and
neutrons) which make up the nucleus.