The Foundations of Chemistry

1 megaelectron volt (MeV)1.60
 10 ^13 J and 1 joule (J)1 kgm^2 /s^2

Let’s use the value of mfor^35 Cl atoms to calculate their nuclear binding energy.

EXAMPLE 26-2 Nuclear Binding Energy

Calculate the nuclear binding energy^35 Cl in (a) kilojoules per mole of Cl atoms, (b) kilo-

joules per gram of Cl atoms, and (c) megaelectron volts per nucleon.

Plan

The mass deficiency that we calculated in Example 26-1 is related to the binding energy by

the Einstein equation.

Solution

The mass deficiency is 0.321 g/mol3.21
 10 ^4 kg/mol.

(a)BE(m)c^2 
(3.00
 108 m/s)^2 2.89
 1013

2.89
 1013 J/mol^35 Cl atoms 2.89
 1010 kJ/mol of^35 Cl atoms

(b) From Example 26-1, the actual mass of^35 Cl is

or

We use this mass to set up the needed conversion factor.

BE
8.26
 108 kJ/g^35 Cl atoms

(c) The number of nucleons in oneatom of^35 Cl is 17 protons18 neutrons35 nucleons.

1 mol^35 Cl atoms



34.9689 g^35 Cl atoms

2.89
 1010 kJ



mol of^35 Cl atoms

34.9689 g



mol^35 Cl atoms

34.9689 amu

 35

Cl atom

kgm^2 /s^2



mol^35 Cl atoms

3.21
 10 ^4 kg



mol^35 Cl atoms

26-3 Nuclear Stability and Binding Energy 1007

BE

 8.57 MeV/nucleon

1 35 Cl atom



35 nucleons

1 mol^35 Cl atoms



6.022
 10 23 35Cl atoms

1 MeV



1.60
 10 ^13 J

1000 J



kJ

2.89
 1010 kJ



mol of^35 Cl atoms

You should now work Exercises 14 and 16.

The nuclear binding energy of a mole of^35 Cl nuclei, 2.89
 1013 J/mol, is an enor-

mous amount of energy—enough to heat 6.9
 107 kg (
76,000 tons) of water from

0°C to 100°C! Stated differently, this is also the amount of energy that would be required

to separate 1 mole of^35 Cl nuclei into 17 moles of protons and 18 moles of neutrons. This

has never been done.

Figure 26-2 is a plot of average binding energy per gram of nuclei versus mass number.

It shows that nuclear binding energies (per gram) increase rapidly with increasing mass

number, reach a maximum around mass number 50, and then decrease slowly. The nuclei

with the highest binding energies (mass numbers 40 to 150) are the most stable. Large

amounts of energy would be required to separate these nuclei into their component

The mass number, Z,is equal to the

number of nucleons in one atom.

Some unstable radioactive nuclei do

emit a single proton, a single neutron,

or other subatomic particles as they

decay in the direction of greater

stability. None decomposes entirely

into elementary particles.