Page 457 - Schaum's Outline of Theory and Problems of Applied Physics

442 NUCLEAR PHYSICS [CHAP. 36

Table 36-1. The Four Fundamental Interactions

Interaction Range Relative Strength Role in Universe

Strong Approx. 10 −15 m 1 Holds protons and neutrons together to
form atomic nuclei.
Electromagnetic Infinite Approx. 10 −2 Determines structures of atoms,
molecules, solids, and liquids; is an
important factor in the astronomical
universe.
Weak Approx. 10 −17 m Approx. 10 −13 Helps determine compositions of atomic
nuclei.
Gravitational Infinite Approx. 10 −40 Assembles matter into planets, stars, and
galaxies.

SOLVED PROBLEM 36.2
State the number of protons and neutrons in the following nuclei:
6 12 36 137
3 Li 6 C 16 S 56 Ba
A
A nucleus designated X contains Z protons and A − Z neutrons. Accordingly, the numbers of protons and
Z
neutrons in the given nuclei are as follows:
6 Li : 3 protons, 3 neutrons
3
12 C : 6 protons, 6 neutrons
6
36 S : 16 protons, 20 neutrons
16
137 Ba : 56 protons, 81 neutrons
56

SOLVED PROBLEM 36.3
35
37
Ordinary chlorine is a mixture of 75.53 percent of the Cl isotope and 24.47 percent of the Cl isotope.
17 17
The atomic masses of these isotopes are, respectively, 34.969 and 36.966 u. Find the average atomic mass
of ordinary chlorine.
The procedure is to multiply the mass of each isotope by the proportion of the whole it represents and then to
add the results. Thus we obtain
(0.7553)(34.969 u) + (0.2447)(36.966 u) = 35.458 u

which is the average atomic mass of ordinary chlorine quoted in chemical tables.

BINDING ENERGY
The mass of an atom is always less than the sum of the masses of the neutrons, protons, and electrons of which it
is composed. The energy equivalent of the missing mass is called the binding energy of the nucleus; the greater
its binding energy, the more stable the nucleus. The mass defect m of a nucleus with Z protons and N neutrons
may be found from its atomic mass m by using the formula

m = Zm H + Nm n − m