Page 297 - Theory and Problems of BEGINNING CHEMISTRY

286 NUCLEAR REACTIONS [CHAP. 19

and can easily get close to the nuclear target. (A report was made in 1989 of a “cold fusion” reaction—a fusion
reaction at ordinary temperatures with relatively little energy input—but that report has not yet been confirmed.)
The stars get their energy from fusion reactions at extremely high temperatures.
The mass of matter at rest is referred to as its rest mass.When matter is put into motion, its mass increases
corresponding to its increased energy. The extra mass is given by
E = mc 2

When a nuclear event takes place, some rest mass is converted to extra mass of the product particles because of
their high speed or to the mass of photons of light. While the total mass is conserved in the process, some rest
mass (i.e., some matter) is converted to energy.
2
Nuclear binding energy is the energy equivalent (in E = mc ) of the difference between the mass of the
nucleus of an atom and the sum of the masses of its uncombined protons and neutrons. For example, the mass of a
4
2 He nucleus is 4.0015 amu. The mass of a free proton is 1.00728 amu, and that of a free neutron is 1.00866 amu.
The free particles exceed the nucleus in mass by
2(1.00728 amu) + 2(1.00866 amu) − 4.0015 amu = 0.0304 amu
This mass has an energy equivalent of 4.54 × 10 −12 J for each He nucleus. You would have to put in that much
energy into the combined nucleus to get the free particles; that is why that energy is called the binding energy.
The difference in binding energies of the reactants and products of a nuclear reaction can be used to calculate
the energy which the reaction will provide.

7
EXAMPLE 19.11. The mass of a Li nucleus is 7.0154 amu. Using this value and those given above, calculate the energy
7
given off in the reaction of 1 mol of Li:
4
7 Li + H −→ 2 He
1
Ans. A mole each of the reactant nuclei has a mass of 7.0154 g + 1.00728 g = 8.0227 g. The product has a mass of
2(4.0015 g) = 8.0030 g. The difference in mass, 0.0197 g, has an energy equivalent to
2
12
2
8
E = mc = (1.97 × 10 −5 kg)(3.00 × 10 m/s) = 1.77 × 10 J
1
7
More than 1 billion kilojoules of energy is produced from a mole of Li nuclei plus a mole of H nuclei. (Burning a
5
mole of carbon in oxygen yields 3.93 × 10 J.)
Solved Problems
INTRODUCTION
19.1. What is the difference between C and 12 C?
Ans. The first symbol stands for the naturally occurring mixture of isotopes of carbon; the second stands for only
one isotope—the most common one.
19.2. The alchemists of the middle ages spent years and years trying to convert base metals such as lead to
gold. Is such a change possible? Why did they not succeed?
Ans. Base metals can be changed to gold in nuclear reactions, but not in ordinary chemical reactions, since both are
elements. (The process costs much more than the gold is worth, however.) The alchemists never succeeded
because they could not perform nuclear reactions. (Indeed, they never dreamed of their existence.)

NATURAL RADIOACTIVITY
19.3. In a nuclear equation, the subscripts are often omitted, but the superscripts are not. Where can you look
to find the subscripts? Why can you not look there for the superscripts?
Ans. You can look at a periodic table for the atomic numbers, which are the subscripts. You cannot look at the
periodic table for the superscripts, because mass numbers are not generally there. (Mass numbers for the