Nuclear physics is a big topic, embracing all of the following:
- The nucleus - protons and neutrons, mass unit and nuclear radius
- Fundamental forces - including the strong nuclear force
- Nuclear radiation - types of particle and their properties
- Nuclear decay - calculating how the number of nuclei change over time
- Strong nuclear force - binding energy and mass defect
- Fission and fusion - processes and stability
Key Concepts
Protons and neutrons
All nuclei are made of nucleons, two types of particle: protons and neutrons. They have almost the same mass.
- Protons have a positive charge (and is the same as the hydrogen nucleus)
- Neutrons have no charge
On the Periodic table and in nuclear equations, we use symbols to represent the numbers of protons and neutrons in nuclear reactions:
A is the nucleon number = protons + neutrons (approximately equal to the mass)
Z is the atomic number = protons (Ze equals the charge in Coulombs)
N is the neutron number = neutrons (A - Z)
A typical atomic symbol on the periodic table (for element 'C'): 
Elements are defined by the number of protons. All atoms of a given element therefore have the same Z but can have different N. This dictates the chemical properties of a given element due to the particular nuclear charge.
Isotopes of an element have the same number of protons but different number of neutrons. Isotopes have the same chemical properties but different physical properties (e.g boiling point).
A neutral atom has the same number of electrons as protons. If the number is different the atom will have a net charge. A charged particle is called an ion.
Unified mass unit (u)
Since the mass of nuclei is based on multiples of protons and neutrons, which themselves have masses in the order of 10-27 kg, it is sensible to define a unit for the nuclear scale: unified mass unit.
The unified mass unit is the mass of \(1\over 12\)th of the mass of an atom of carbon-12:
1u = 1.66054 x 10-27 kg
This gives the following masses for our nucleons:
| Proton | 1.00728 u |
| Neutron | 1.00866 u |
Nuclear radius
Nuclei are too small for us to observe. However, we can get an approximation by finding the closest distance of a approach when a positive alpha particle is fired at a nucleus.
If the alpha particle has charge +2e, mass m and velocity v, the closest it will approach a nucleus of proton number Z is governed by the following equation:
The radius of the nucleus is found to be in the order of 10-15 m (the overall atomic radius is about 10-10 m).
The physics course to date has taught us about two fundamental forces:
- Electromagnetic - acts between charged particles, carried by photons
- Gravity - acts between masses, carried by gravitons
Nucleons are held together by the strong nuclear force. This has a very short range and takes over the repulsive electromagnetic force between charges at short range.
| Force | Strength (relative) | Range |
| Nuclear | 1 | 10-15 m |
| Electromagnetic | 10-2 | infinite |
| Gravity | 10-38 | infinite |
As well as undergoing fission, large nuclei may also become more stable by releasing small ionising particles. This process is known as nuclear radiation and isotopes that release particles are referred to as radioactive.
We can detect nuclear radiation by several methods:
- Photographic film - changes colour when radiation is absorbed. This can be used to produce safety badges for workers in nuclear power stations, as it will darken when exposed to radiation.
- Ionisation chamber - when ionising radiation enters the chamber, the gas present becomes ionised. This produces electrons that can cause a current to flow. A similar principle is used in household smoke detectors, where a radioactive isotope is always present to cause a current - if this is blocked by large smoke particles, an alarm is sounded.
- Geiger-Müller tube and counter - this apparatus contains a high voltage and an inert (unreactive) gas. When ionising radiation enters, the particles of gas become charged and electrons are freed. These are accelerated by the voltage and an electrical pulse is produced.
- Cloud chamber - contains a supersaturated gas. When ionisation occurs, the ions act as small condensation locations, and tracks are formed through the gas.
A - alpha particle
B - beta particle
The types of ionising radiation that can be released by radioactive isotopes are:
- Alpha
- Beta
- Gamma
Alpha (\(\alpha\))
Alpha particles consist of a helium nucleus (2p+ 2no). Their relatively large mass and charge mean that they are the most ionising type of radiation. However, this also has the effect that they can only penetrate 2-3 cm of air and they are absorbed fully by a sheet of paper.
Alpha decay example: 
From this spectrum we can deduce that there are two alpha energies: one at 5.5 MeV and the other at about 5.45 MeV.
According to the conservation of momentum and energy, this isn't possible unless the nucleus holds onto some energy.
Beta (\(\beta\))
Beta particles consist of an electron. Electrons are not normally found in the nucleus, but are released during the process of beta decay, when when a neutron changes into a proton plus an electron. Beta particles are absorbed by a sheet of aluminium foil.
Beta decay example:
The \(\bar{\nu}\) symbol represents an anti-electron neutrino. The beta energy spectrum provides evidence of the neutrino, which takes some of the kinetic energy:
- Mass - almost nothing
- Charge - zero
- Spin - \(1\over 2\)
Note that both alpha and beta radiation produce new elements.
Gamma (\(\gamma\))
Gamma particles are photons of high energy electromagnetic radiation (the same as the gamma we are familiar with from the electromagnetic spectrum). Gamma photons are highly penetrating, only absorbed by several metres of concrete or thick sheets of lead. However, they are the least ionising of these three types of radiation.
Gamma radiation is emitted when there are energy changes within the nucleus, for example, following alpha or beta decay. It does not change the composition of the nucleus, but this change in stability can be indicated by an asterisk (*) on the left hand nucleus of the nuclear equation.
Decay constant
Radioactive decay is a random process. This means that:
- We do not know exactly when the next nucleus will decay
- We do not know exactly which the next nucleus to decay will be
- We can predict how many nuclei are likely to decay in a given time period
The rate of decay is proportional to the number of nuclei:
\({\mathrm{d} N\over \mathrm{d}t} \propto -N\)
\({\mathrm{d} N\over \mathrm{d}t} = -\lambda N\)
λ is the decay constant, an unchanging value for a given isotope. The decay constant is large if the nucleus is unstable.
Solving the differential equation gives:
\(N_t=N_0\mathrm{e}^{-\lambda t}\)
- Nt is the number of nuclei at time t
- N0 is the original number of nuclei
This function can be plotted in GeoGebra. Observe the changes to the curve when you vary N0 and λ.
Activity
Activity (A) is defined as the number of particles emitted per second. This is measured in Bequerel (Bq). This is dimensionally equivalent to s-1.
Activity and number of nuclei are proportional. Therefore, activity also follows the exponential decay relationship:
\(A_t=A_0\mathrm{e}^{-\lambda t}\)
Half life
Half life (\(t_{1\over 2}\)) is the time for half of the nuclei of an isotope to decay. This is equal to the time for the activity to halve.
Half life is a constant for a given isotope, and a mathematical outcome of exponential decay.
If \(t=t_{1\over 2}\) then \(N = {N_0 \over 2}\). Substituting this into the decay equation shows that:
\(t_{1\over 2}={\ln2 \over \lambda}\)
\(\lambda={\ln2 \over t_{1\over 2}}\)
NB: When in doubt in a nuclear decay exam question, start by finding the decay constant. You are likely to be given the half life.
When particles of matter meet the equivalent particles of antimatter, they annihilate. This led Einstein to his famous mass-energy formula.
\(E=mc^2\)
c = the speed of light in a vacuum (3 x 108 ms-1)
The signficance of this equation is that we can calculate the amount of energy required to be converted into the mass of a particle, and vice versa.
As more and more nucleons combine in the nucleus, the binding energy increases due to the increased presence of the strong force. To determine whether the nucleus of an isotope is stable, we divide the binding energy by the number of nucleons present.
When binding energy per nucleon is plotted against nucleon number, we find that a curve is produced:
- Small nuclei are unstable - they would need to gain binding energy to become more stable
- Isotopes of iron and nickel are the most stable, with binding energies per nucleon of almost 9 MeV
- Very large nuclei are unstable - they would need to lose nucleons to become more stable
Fusion
Nuclear fusion is the combining of two small nuclei to produce one, more massive, nucleus. This increases the binding energy per nucleon, for example:
Nuclear fusion reactions release energy as the binding energy required to separate the nucleons in the nucleus increases, calculated using the mass defect. However, since nuclei are positive, they repel each other. This means that they must be thrown together with high speed to get them close enough for the nuclear force to pull them together.
Fission
Nuclear fission is the splitting of one massive nucleus into two, similarly sized, daughter nuclei. This increases the binding energy per nucleon, for example:
Like for nuclear fusion, the energy released can be found from the mass defect. Find out more in the Energy sources topic.
How much of Nuclear physics have you understood?
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