Nuclear Reaction Fundamentals

Nuclear Reaction Fundamentals

While an in-depth understanding of the physics of the nucleus can be a

prodigious undertaking, a relatively simple model of the nucleus will

suffice for our study of nuclear power reactors. The standard model of

an atom consists of a very dense positively charged nucleus, surrounded

by negatively charged orbiting electrons. Compared to the

size of atoms, with diameters of roughly 10^-8 cm, the size of the

nucleus is very small, of the order of10^-12 cm. For modeling purposes

we consider a nucleus to be made up of N neutrons and Z protons.

Both are referred to as nucleons, thus the nucleus has NþZ nucleons.

The number of protons, Z, is the atomic number; it determines an

atom’s chemical properties, while NþZ is its atomic weight. Nuclei

with the same atomic number but different atomic weights, due to

different numbers of neutrons, are isotopes of the same chemical

element. We refer to a nucleus as N+ZZX, where X is the symbol used

in the periodic table to designate the chemical element

Reaction Equations

Nuclear reactions are written as

A+ B = C + D ..................(1.1)

An example of a nuclear reaction is

He +Li =Be+H ...................(1.2)

This equation does not tell us how likely the reaction is to take place,

or whether it is exothermic or endothermic. It does, however, illustrate

two conservation conditions that always hold: conservation of

charge (Z) and conservation of nucleons (N+Z). Conservation of

charge requires that the sum of the subscripts on the two sides

of the equation be equal, in this case 2+3=4+1. Conservation of

nucleons requires that the superscripts be equal, in this case

4+6=9+1.

Nuclear reactions for the most part take place in two stages. First

a compound nucleus is formed from the two reactants, but that

nucleus is unstable and so divides, most often into two components.

This being the case, we might write Eq. (1.2) in two stages:

He + Li = B --> Be + H ...........................(1.3)

However, in most of the reactions that we will utilize the compound

nucleus disintegrates instantaneously. Thus no harm is done in

eliminating the intermediate step from the reaction equation. The

exception is when the compound nucleus is unstable but disintegrates

over a longer period of time. Then, instead of writing a single

equation, such as Eq. (1.3), we write two separate reaction equations.

For example, when a neutron is captured by indium, it emits only a

gamma ray:



The gamma ray has neither mass nor charge. Thus we give it both

super- and subscripts of zero: of gamma ray

. Indium-117 is not a stable nuclide but

rather undergoes radioactive decay, in this case the indium decays to

tin by emitting an electron, and an accompanying gamma ray:

In -->Sn + e + gamma ray ......................(1.5)

The electron is noted by e, with a subscript of 1, since is has the

opposite charge of a proton and a superscript of zero since its mass is

only slightly more than one two-thousandths of the mass of a proton

or neutron. A rudimentary way of looking at the nuclear model would

be to view the electron emission as resulting from one of the neutrons

within the nucleus decomposing into a proton and an electron.

Decay reactions such as Eq. (1.5) take place over time and are

characterized by a half-life, referred to as t1/2 . Given a large number

of such nuclei, half of them will decay in a time span of t1/2 , threefourths

of them in 2t1/2 , seven-eighths of them in 3t1/2 , and so on.

The half-life of indium-117 is 54 minutes. Half-lives vary over many

orders of magnitude, depending on the nuclide in question. Some

radioactive materials with very long half-lives appear naturally in

the surface of the earth. For example,

U --> Th + He .............................(1.6)

with t1/2 =2.45*10^-5 years. We will return to the mathematical

description of half-lives and radioactive decay later in the chapter.

Gamma rays are sometimes omitted from reaction equations;

since they carry neithermass nor charge they do not affect the nucleon

and charge balances that we have thus far discussed. Gamma rays,

however, are important in the energy conservation law that we will

discuss subsequently. Their role may be understood as follows. Following

a nuclear collision, reaction, or radioactive decay the nucleus

generally is left in an excited state. It then relaxes to its ground or

unexcited state by emitting one or more gamma rays. These rays are

emitted at distinct energies, corresponding to the quantum energy

levels of the nucleus. This nuclear phenomenon is analogous to the

situation in atomic physics where an orbital electron in an excited

state emits a photon as it drops to its ground state. Both gamma rays

and photons are electromagnetic radiation. However, they differ

greatly in energy. For while the photons emitted from the relaxation

of orbital electrons typically are in the electron volt range, the energies

of gamma rays are measured in millions of electron volts.

One remaining nuclear radiation, which we have not mentioned, is

the neutrino. In conjunction with electron emission a neutrino is created,

and carries off a part of the reaction energy. Since neutrinos do not

interact with matter to any significant extent, the energy they carry away

is for all practical purposes lost. However, they must be included in the

energy conservation considerations of the following section.

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