bei48482_FM

proton. The required energy indeed turns out to be 2.224 MeV (Fig. 11.11). When

less energy than 2.224 MeV is given to a^21 H nucleus, the nucleus stays together. When

the added energy is more than 2.224 MeV, the extra energy goes into kinetic energy of

the neutron and proton as they fly apart.

Deuterium atoms are not the only ones that have less mass than the combined

masses of the particles they are composed of—allatoms are like that. The energy equiv-

alent of the missing mass of a nucleus is called the binding energyof the nucleus. The

greater its binding energy, the more the energy that must be supplied to break up the

nucleus.

The binding energy Ebin MeV of the nucleus AZX, which has NAZneutrons,

is given by

Eb[Zm(^11 H)Nm(n)m(ZAX)](931.49 MeV/u) (11.7)

where m(^11 H) is the atomic mass of^11 H, m(n) is the neutron mass, and m(ZAX) is the

atomic mass of AZX, all in mass units. As mentioned before, atomic masses, not nuclear

masses, are used in such calculations; the electron masses subtract out.

Nuclear binding energies are strikingly high. The range for stable nuclei is from

2.224 MeV for^21 H (deuterium) to 1640 MeV for^20983 Bi (an isotope of the metal bis-

muth). To appreciate how high binding energies are, we can compare them with more

familiar energies in terms of kilojoules of energy per kilogram of mass. In these units,

a typical binding energy is 8  1011 kJ/kg—800 billion kJ/kg. By contrast, to boil water

400 Chapter Eleven

Figure 11.11The binding energy of the deuterium nucleus is 2.224 MeV. A gamma ray whose energy

is 2.224 MeV or more can split a deuterium nucleus into a proton and neutron. A gamma ray whose

energy is less than 2.224 MeV cannot do this.

Deuterium

nucleus

Proton

Neutron

2.224-MeV

gamma ray

=

Hydrogen

atom

Deuterium

atom

Neutron mn = 1.0087 u

mH = 1.0078 u

mD = 2.0141 u

2.0165 u

Figure 11.10The mass of a deuterium atom (^21 H) is less than the sum of the masses of a hydrogen

atom (^11 H) and a neutron. The energy equivalent of the missing mass is called the binding energy of

the nucleus.

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