The Foundations of Chemistry

NUCLEAR STABILITY AND BINDING ENERGY

Experimentally, we observe that the masses of atoms other than^11 H are always lessthan
the sum of the masses of their constituent particles. We now know why this mass deficiency
occurs. We also know that the mass deficiency is in the nucleus of the atom and has nothing
to do with the electrons; however, because tables of masses of isotopes include the electrons, we
shall also include them.
The mass deficiency,
m,for a nucleus is the difference between the sum of the
masses of electrons, protons, and neutrons in the atom (calculated mass) and the actual
measured mass of the atom.

m(sum of masses of all e, p, and n^0 )(actual mass of atom)

For most naturally occurring isotopes, the mass deficiency is only about 0.15% or less of
the calculated mass of an atom.

EXAMPLE 26-1 Mass Deficiency

Calculate the mass deficiency for chlorine-35 atoms in amu/atom and in g/mol atoms. The
actual mass of a chlorine-35 atom is 34.9689 amu.

Plan

We first find the numbers of protons, electrons, and neutrons in one atom. Then we deter-
mine the “calculated” mass as the sum of the masses of these particles. The mass deficiency is
the actual mass subtracted from the calculated mass. This deficiency is commonly expressed
either as mass per atom or as mass per mole of atoms.

26-3

120

100

80

60

40

20

20 40 60

1:1 ratio

Neutron-poor

nuclei

Neutron-rich

nuclei

1.2

80

Number of protons

Number of neutrons

1.4

1.5

Figure 26-1 A plot of the number

of neutrons versus the number of

protons in stable nuclei. As atomic

number increases, the N/Zratio (the

decimal fractions) of the stable nuclei

increases. The stable nuclei are

located in an area known as the band

of stability. Most radioactive nuclei

occur outside this band.

Do you remember how to find the

numbers of protons, neutrons, and

electrons in a specified atom? Review

Section 5-7.