Page 458 - Schaum's Outline of Theory and Problems of Applied Physics

CHAP. 36] NUCLEAR PHYSICS 443

where m H , the mass of the hydrogen atom (which consists of a proton and an electron), is
m H = 1.007825 u

To find the binding energy in megaelectronvolts (MeV), the usual unit, m can be multiplied by the conversion
factor 931 MeV/u.

SOLVED PROBLEM 36.4
16
The atomic mass of O is 15.9949 u. (a) What is its binding energy? (b) What is its binding energy per
8
nucleon?
16
(a) The O contains 8 protons and 8 neutrons in its nucleus. The mass of 8 H atoms is 8m H = (8)(1.007825) u =
8
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8.0626 u, and the mass of 8 neutrons is 8m n = (8)(1.008665) u = 8.0693 u. Hence the mass deficit is Ois
8
m = (8.0626 + 8.0693) u − 15.9949 u = 0.1370 u
and since 1 u = 931 MeV, the binding energy is
E = (0.1370 u)(931 MeV/u) = 127.5 MeV
(b) There are 16 nucleons in 16 8 O, so the binding energy per nucleon is 127.6 MeV/16 nucleons = 7.97 MeV
per nucleon.

SOLVED PROBLEM 36.5
The binding energy of 20 Ne is 160.6 MeV. Find its atomic mass.
10
20
The Ne contains 10 protons and 10 neutrons in its nucleus. The mass of 10 H atoms and 10 neutrons is
10
m 0 = 10.07825 u + 10.08665 u = 20.1649 u
The mass equivalent of 160.6 MeV is
160.0 MeV
m = = 0.1725 u
931 MeV/u
20
and so the mass of the Ne atom is
10
m = m 0 − m = 20.1649 u − 0.1725 u = 19.9924 u

NUCLEARREACTIONS
Nuclei can be transformed into others of a different kind by interaction with each other. Since nuclei are all
positively charged, a high-energy collision is necessary between two nuclei if they are to get close enough
together to react. Because it has no charge, a neutron can initiate a nuclear reaction even if it is moving slowly.
In any nuclear reaction, the total number of neutrons and the total number of protons in the products must be
equal to the corresponding total numbers in the reactants.

FISSION AND FUSION
Nuclei of intermediate size have the highest binding energies per nucleon (Fig. 36-1) and therefore are more
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stable than lighter and heavier nuclei. The highest binding energy per nucleon is found in the iron nucleus Fe.
26
If a heavy nucleus is split into two smaller ones, the greater binding energy of the latter means that energy will
be liberated. This process is called nuclear fission. Certain very large nuclei, such as 235 U, undergo fission when
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they absorb a neutron. Since the products of the fission include several free neutrons as well as two daughter