Nuclear Physics

5.1.1 The atom

An atom has a tiny, dense, positively charged nucleus at its centre. Electrons (negatively charged) orbit the nucleus.

A neutral atom has equal numbers of protons and electrons, so the charges cancel.

The alpha-particle scattering experiment

In this experiment, a beam of alpha particles (positive) was fired at a very thin sheet of gold foil, and a detector was moved round to count the particles at different angles.

So the experiment provides evidence for a very small nucleus surrounded by mostly empty space, a nucleus that contains most of the mass of the atom, and a nucleus that is positively charged.

5.1.2 The nucleus

The nucleus is made of protons and neutrons, which are together called nucleons.

An atom becomes an ion when it gains or loses electrons:

• losing electrons gives a positive ion (more protons than electrons);
• gaining electrons gives a negative ion.

A nuclide is a particular type of nucleus. It is written in nuclide notation: ${}^{A}_{Z}\text{X}$, where X is the chemical symbol.

• Protons: $Z = 6$.
• Neutrons: $A - Z = 14 - 6 = 8$.
• Electrons in a neutral atom: $6$.

$235 - 92 = 143$

Isotopes are atoms of the same element (the same $Z$) with different numbers of neutrons (different $A$). They have the same chemical properties. Carbon-12 and carbon-14 are isotopes of carbon: both have 6 protons, but they have 6 and 8 neutrons. An element can have more than one isotope.

5.2.1 Detection of radioactivity

• Alpha particles can be detected with a cloud chamber (they leave visible tracks) or a spark counter.
• Beta particles and gamma radiation are detected with a Geiger–Müller (GM) tube connected to a counter.

The counter gives the count rate, measured in counts per second or counts per minute.

Background radiation

Background radiation is the low level of radiation that is always present. The main sources are:

• radon gas in the air (from rocks),
• rocks and buildings,
• food and drink,
• cosmic rays from space.

To measure only a source, first measure the count rate with no source present (the background), then with the source, and subtract.

$85 - 15 = 70\ \text{counts per minute}$

5.2.2 The three types of emission

Some nuclei are unstable and give out radiation to become more stable. The emission is spontaneous (it is not caused by anything outside the nucleus) and random (we cannot tell when a particular nucleus will decay, or in which direction the radiation will go).

Deflection in fields.

• In an electric field, alpha particles are deflected slightly towards the negative plate, beta particles are deflected more (they are much lighter) towards the positive plate, and gamma rays are not deflected because they have no charge.
• In a magnetic field, alpha and beta are deflected in opposite directions (they have opposite charges, and you can find the direction with Fleming's left-hand rule), and gamma rays are not deflected.

5.2.3 Radioactive decay

Radioactive decay is a change in an unstable nucleus that can give out $\alpha$-particles or $\beta$-particles, and/or $\gamma$-radiation. It is spontaneous and random.

Decay equations. In an equation, the total of the nucleon numbers (top) and the total of the proton numbers (bottom) must each be the same on both sides.

• Alpha decay. The nucleus loses 2 protons and 2 neutrons. $A$ decreases by 4 and $Z$ decreases by 2.

${}^{241}_{95}\text{Am} \;\to\; {}^{237}_{93}\text{Np} + {}^{4}_{2}\alpha$

• Beta decay. A neutron in the nucleus changes into a proton and an electron, and the electron is emitted. $A$ stays the same and $Z$ increases by 1.

${}^{14}_{6}\text{C} \;\to\; {}^{14}_{7}\text{N} + {}^{0}_{-1}\beta$

• Gamma emission. A nucleus that has just emitted an alpha or beta particle often has extra energy, and gets rid of it as gamma radiation. $A$ and $Z$ do not change.

The daughter nucleus has nucleon number $226 - 4 = 222$ and proton number $88 - 2 = 86$, which is radon (Rn):

${}^{226}_{88}\text{Ra} \;\to\; {}^{222}_{86}\text{Rn} + {}^{4}_{2}\alpha$

5.2.4 Fission and fusion

Fusion

Fusion is the joining of two small nuclei to make a larger nucleus, releasing energy. It needs very high temperatures and pressures, because the nuclei repel each other. Fusion is the energy source for stars: the Sun fuses hydrogen into helium.

Fission

Fission is the splitting of a large nucleus. A uranium-235 nucleus absorbs a neutron and splits into two smaller daughter nuclei, plus two or more neutrons, and releases energy.

Chain reaction. The neutrons given out can be absorbed by other uranium-235 nuclei and make them split too. If each fission leads to more than one further fission, the reaction grows rapidly and can run out of control, as in a nuclear bomb.

In a nuclear reactor the chain reaction is controlled:

5.2.5 Half-life

$9.0$ hours is $\dfrac{9.0}{3.0} = 3$ half-lives, so the count rate is halved three times:

$800 \to 400 \to 200 \to 100\ \text{counts per minute}$

$12$ days is $3$ half-lives: $80 \to 40 \to 20 \to 10$, so $10\ \text{g}$ is left.

Carbon dating

Living things take in carbon, including a small constant fraction of radioactive carbon-14. When a living thing dies, no more carbon-14 is taken in, and what is there decays with a half-life of about $5700$ years. Measuring the activity of carbon-14 in an old object and comparing it with that of living material shows how long ago it died.

A quarter is two halvings, so two half-lives: $2 \times 5700 = 11\,400$ years.

Choosing an isotope for a job

The right isotope depends on the type of radiation it emits and its half-life.

5.2.6 Safety precautions

Ionising radiation can damage or kill cells, and mutate the DNA in them, which can lead to cancer.

Radioactive materials are moved, used and stored safely by:

• reducing the time of exposure (work quickly, and keep sources locked away when not in use);
• increasing the distance between the source and the person (use tongs or long handles, because the radiation gets weaker with distance);
• using shielding to absorb the radiation (lead or thick concrete walls, and sources kept in lead-lined containers).

Sources are clearly labelled, kept in locked, shielded stores, and people who work with them wear badges that record how much radiation they have received.