Nuclear Physics

Nuclear Model of the Atom

The nuclear model of the atom consists of a small nucleus containing protons (positively charged) and neutrons (neutrally charged). The atom is surrounded by electrons, which are negatively charged.

The nucleus is held together by the strong nuclear force. The strong nuclear force (also known as just the strong force) is a force which operates between neutrons, and is very short-range. The strong nuclear force must oppose the electrostatic repulsive forces between the protons in the nucleus.

When a nucleus is too unstable, it may spontaneously break apart, which is known as radioactive decay.

Half-Life

The half-life of a radionuclide is a number representing the rate of decay. The half-life is the amount of time it takes for half of a sample to decay. The following equation is used:

$$N=N_0{\left(\frac{1}{2}\right)}^n$$

where $N$ is the remaining number of undecayed atoms in the sample, $N_0$ is the original number of atoms in the sample and $n$ is the number of half-lives that have elapsed.

We can also use the following equation:

$$t=n{t}_{\frac{1}{2}}$$

where $t$ is the time that has elapsed, $n$ is the number of half lives that have elapsed and $t_{\frac{1}{2}}$ is the half-life.

Types of Radiation

The types of radiation are as follows.

Alpha

Alpha radiation results when a nuclide decays to form a helium nucleus and another nuclide.

$$\text{Z}\text{A}\text{X}⟶42\alpha +\text{Z}-4\text{A}-2\text{Y}$$

Alpha radiation has the following properties:

• Short range (on the order of cm), and easily stopped: it is easily the largest and most massive type of radiation.
• Travels at about $5\%$ the speed of light

Beta

Beta radiation results when a proton or neutron in the nucleus transmutes into a neutron or proton, releasing an electron or positron.

There are two types of Beta decay.

Beta Plus

$$\text{Z}\text{A}\text{X}⟶\text{Z}\text{A}-1\text{Y}+0+1\text{e}+v$$

Beta Minus

$$\text{Z}\text{A}\text{X}⟶\text{Z}\text{A}+1\text{Y}+0-1\text{e}+\overline{v}$$

(The electron is sometimes represented as ${\beta }^{+}or{\beta }^{-}$.)

Beta radiation has the following properties:

• Medium range (metres), and slightly more difficult to stop than alpha radiation
• Travels at about $40$ to $70\%$ the speed of light.

Gamma

Gamma decay occurs when a nucleus has a high energy and is therefore unstable, usually immediately after undergoing decay.

$$\text{Zm}\text{A}\text{X}⟶\text{Z}\text{A}\text{X}+00\gamma$$

Gamma radiation has the following properties:

• Long range, and very difficult to stop
• Travels at the speed of light - it is electromagnetic radiation

Absorbed Dose and Equivalent Dose

The absorbed dose and equivalent dose are used in the following equations:

$$AD=\frac{E}{m}ED=AD\ast QF$$

where $AD$ is absorbed dose, $ED$ is equivalent dose, $E$ is energy, $m$ is mass, and $QF$ is the quality factor of the type of radiation (a constant).

Absorbed Dose has units $Gy$, or Grays. Equivalent Dose has units $Sv$, or Sieverts. Both of these units are dimensionally equivalent but refer to different things.

Mass Defect

The mass defect of an atom is the difference between its actual mass and the combined masses of its neutrons, protons and electrons. The mass defect is equal to the binding energy in the nucleus. Dividing the binding energy by the number of nucleons (named binding energy by nucleon) can give a measure of the stability of the nucleus.

The mass defect of a nuclear equation can be calculated by subtracting the mass of the products from the mass of the reactants, and can be used as a measure of the amount of energy released.

Nuclear Fission

In nuclear fission, one atom decomposes into multiple other atoms. The first atom is called the 'parent' and the produced atoms are called the 'daughters'.

Neutron-induced nuclear fission is a reaction in which a heavy, unstable nuclide captures a neutron, thus causing it to undergo nuclear fission and release energy.

Chain Reactions

A chain reaction occurs when each fission event requires at most as many neurons as it requires, i.e. the reaction is self-sustaining. The critical mass of a substance is the mass required for a reaction to sustain itself, i.e. for one neutron on average to be produced per fission event.

Thermal and Fast-moving neutrons

Thermal neutrons travel relatively slowly. Both $235\text{U}$ and $238\text{U}$ are efficient at capturing thermal neutrons (although $235\text{U}$ is more efficient).

Fast-moving neutrons travel at high speed, and are usually emitted during fission. $235\text{U}$ is inefficient at capturing fast-moving neutrons, whereas $238\text{U}$ is efficient at capturing them.

If $235\text{U}$ absorbs a neutron, it will result in a fission event; if $238\text{U}$ captures a neutron it will not result in a fission event.

Nuclear Fusion

In nuclear fusion, two or more light nuclides combine to form a heavy nuclide. Very large amounts of energy are released by nuclear fusion, comparitively to fission, as a greater percentage of mass is transformed to energy.. Enormous amounts of energy are required to start fusion, since for fusion to occur the repulsive electrostatic force between nuclides must be overcome; the nuclides must be brought close enough for the strong nuclear force to take effect.

Nuclear Reactors

Current nuclear reactors mainly use fission, because nuclear fusion requires very high temperatures and no method has yet been found to produce more energy than is used to initiate nuclear fusion.

A nuclear reactor consists of a number of fuel rods and moderators sandwiched in a row. If using uranium fuel, the $235\text{U}$ emits fast-moving neutrons during fission, which $235\text{U}$ is inefficient at absorbing. A moderator's role is to slow down the neutrons to allow the $235\text{U}$ to absorb them (as explained above, $235\text{U}$ is only efficient at absorbing slow-moving neutrons). The moderator must not absorb the neutrons. Water is often used as a moderator; heavy water is the best but is expensive, and graphite is another option which is notable for its low price (and relatively low quality). Control rods absorb neutrons allowing workers to control the fission rate. Moving the control rods up increases the number of neutrons and fission events / rate; moving them down has the opposite effect.