Chapter 6 Reference: The Energy Stored in a Nucleus

The nuclei of atoms remain intact during a

chemical reaction. This suggests that much larger

quantities of energy are required for nuclear changes.

Experimentally, this has proven to be true. Nuclear

reactions usually involve energy changes that are

over a million times greater than those found in

chemical reactions. This enormous factor accounts

for the interest in nuclear reactions as a source of

energy.

One such nuclear reaction is represented by the

following equation:

+ → + + 3 + energy

Focusing on the “+ energy” term in the equation,

the numerical value is on the order of 4.5 x 109

kcal/mole of uranium. Compare this to the molar

heat of combustion of carbon at about 94 kcal/mole.

In this case, the energy produce from the nuclear

reaction is on the order of 107 times greater than that

produced from the chemical reaction.

Looking at the nuclear reaction above, the symbol

is the isotopic notation representing the neutron,

one of the fundamental particles present in the

nucleus of the atom. (Reminder: the superscript

refers to the mass number and the subscript refers to

the atomic number.) In the overall reaction, instead

of producing new kinds of substances by the

rearranging and recombining of atoms, the element

uranium has combined with a neutron and split into

two other elements – barium and krypton – plus three

more neutrons. Atoms of a given element are

characterized by their atomic number, the number of

units of positive charge on the nucleus. For one

element to change into another element, the nucleus

must be altered. In the above example, the uranium

nucleus, when reacting with the neutron, splits of

fissions into two other nuclei and, in addition,

releases three more neutrons. The above reaction is

used in an atomic pile, the energy source of a nuclear

power plant. The example shown is only one of the

ways the uranium nucleus can divide. Lanthanum

and bromine nuclei are also produced, cerium and

selenium, and so on, each pair of fission products

being such that the sum of their atomic numbers is

always 92.

In order to determine the products of a nuclear

reaction, it is necessary to pay attention to the

superscripts and subscripts shown with each isotope.

The subscripts refer to the atomic number, or the

number of units of positive charge in the nucleus.

The zero subscript attached to the neutron denotes the

lack of charge on this on this particle. Looking at

just the subscripts,

+ → + + 3

Notice that the sum on each side of the equation is

identical: 92 + 0 = 56 + 36 + (3 x 0). This is

another way of expressing the law of conservation of

charge. (Reminder: Since a neutral atom has the

same number of electrons as it has protons, the

charge from the electrons is also conserved)

In the model of the atom, the nucleus is pictured as

being made up of protons and neutrons. These two

kinds of particles are given the general name

nucleon. The mass number of a nucleus is equal to

the number of nucleons present for a particular

isotope. The superscripts in the equation represent

the mass numbers:

+ → + + 3

The mass numbers are also conserved:

235 + 1 = 141 + 92 + (3 x 1)

This may be rephrased in terms of a rule: The total

number of nucleons in unchanged during nuclear

reactions.

The nuclear reaction is really representing the nuclei

and the particles associated with them. It does not

tell anything about what compound of uranium was

bombarded with neutrons or what compound of

barium is formed. A nuclear equation summarizes

only the nuclear changes. During the nuclear change,

there is much disruption of the other atoms present

due to the tremendous amounts of energy released

Exact Mass Relationships

Although the mass numbers of the proton and

neutron are both one, the masses of these

fundamental particles are not identical. The mass of

one mole of protons is 1.00762 grams whereas the

mass of mole of neutrons is 1.00893 grams. Further

investigation shows that the experimentally measured

mass of the nucleus of any given isotope is not the

exact sum of the masses of protons and neutrons

confined in the nucleus. For example, the mass of

the nucleus of the uranium isotope of mass number

235 is less than the sum of the masses of 92 protons

and 143 neutrons.

One of the consequences of the special theory of

relativity formulated by Albert Einstein in 1905 was

that we came to realize that mass and energy are one

and the same. Although this was a very radical

notion at the time Einstein first presented his theory,

the equation relating mass to energy, E = mc2, has

become very familiar to many since the successful

application of nuclear energy became a part of

modern technology in the 1940’s. In this equation, c

is the speed of light, 3.00 x 1010

cm/second. A small

amount of mass, m, is equivalent to a tremendous

amount of energy. The proportionality constant, c2,

relating mass to energy is numerically, 9.00 x 1020

.

The idea of the relationship between mass and

energy can be used in several ways. The mass of the

nucleus is less than the masses of the 92 protons

and 143 neutrons postulated to be in it. The

difference in mass represents the binding energy

which holds the nucleons together in the nucleus.

The nuclear binding energy can be used as a way to

express the implied decrease in mass. Going back

to a chemical reaction, the combustion of carbon,

C (s) + O2 (g) → CO2 (g) H = -94 kcal

The mass change associated with an energy change

on the order of 102 kcal is about 5 x 10

-9 grams. This

is a quantity far too small to be detected on any

balance capable of weighing out the 12 grams of

carbon and 32 grams of oxygen consumed in the

reaction. Since the chemical “mass defects” are too

small to measure, the amounts are not used for

chemical reactions.

If we wish to gain some idea of the alteration of

mass in a nuclear change, we cannot use the fission

reaction because the exact masses of the nuclei

involved are not known. Let us look at another type

of reaction of possible importance in the production

of nuclear energy:

This reaction is called fusion since nuclei are

combining to form a heavier nucleus. The energy

associated with this change is 4.05 x 108 kcal/mol of

nuclei.

Let us do a little work with the exact masses of the

nuclei. We will simplify it a bit by using the exact

masses of the atoms. This will make no difference,

since the masses of the atoms differ from the nuclear

masses by the masses of the electrons present in each

atom. Since charge is conserved, the number and

character of the electrons does not change between

reactants and products, so there is no difference in the

mass of the electrons. Thus, for the hydrogen-to-

helium reaction:

Reactants: 2.01471 g/mol

3.01701

Sum: 5.03178

Products: 4.00390 g/mol

1.00893

Sum: 5.01283

Mass difference: 5.03178 – 5.01283 = 0.01895 g/mol

Compare this mass difference of 0.02 g/mol for the

nuclear reaction with the approximate 5 x 10-9

g/mol

for the chemical reaction of combustion of carbon.

As a reminder, in nuclear reactions, changes in the

nuclei take place. In a chemical reaction, the nuclei

remain intact and the changes are explainable in

terms of the electrons outside of the nucleus.

Nuclear Decay

Nuclear decay is the spontaneous decomposition

of an unstable nucleus that results in the emission of

ionizing particles and/or radiation. Several types of

decay occur. In all cases, the same rules apply to

these types of nuclear reactions as apply to fission

and fusion: the charge and total number of nucleons

are conserved in a nuclear reaction. For further

information on the types of radioactive decay, refer to

pages 860-862 in your Ebbing/Gammon textbook and

pages 685 – 687 in the Holt textbook.