Welcome to Nuclear Radiation!
In this chapter, we are going to dive into the heart of the atom. We’ll explore why some atoms are unstable, how they release energy, and the mathematical rules that govern radioactive decay. Nuclear physics might sound intimidating, but don't worry—we will break it down piece by piece. Understanding this isn't just for exams; it’s the science behind carbon dating, medical imaging, and the very energy that powers the Sun!
1. Types of Nuclear Radiation
Most atoms are stable, but some have an "unhappy" balance of protons and neutrons. These unstable nuclei become stable by emitting radiation. There are three main types you need to know: Alpha (\(\alpha\)), Beta (\(\beta\)), and Gamma (\(\gamma\)).
Properties of Radiation
Each type of radiation behaves differently based on its nature:
- Alpha (\(\alpha\)): These are helium nuclei (2 protons, 2 neutrons). Because they are relatively big and double-positively charged, they are highly ionising but have a short range (only a few cm in air). They can be stopped by a single sheet of paper.
- Beta (\(\beta\)): These are fast-moving electrons (\(\beta^-\)) or positrons (\(\beta^+\)). They are moderately ionising and can travel about a metre in air. They are stopped by a few millimetres of aluminium.
- Gamma (\(\gamma\)): This is high-energy electromagnetic radiation (waves, not particles). It is weakly ionising because it has no charge, but it is highly penetrating. It can travel long distances in air and requires several centimetres of lead or metres of concrete to be significantly reduced.
Nuclear Equations
When a nucleus decays, we use equations to show what happens. The golden rule is: The total Mass Number (top) and total Atomic Number (bottom) must be the same on both sides.
Example (Alpha Decay): \(_{92}^{238}\text{U} \rightarrow _{90}^{234}\text{Th} + _{2}^{4}\alpha\)
Notice how \(238 = 234 + 4\) and \(92 = 90 + 2\). Simple!
Quick Review: Alpha is a "bully" (big and hits hard/ionises), Beta is a "runner" (smaller and faster), and Gamma is a "ghost" (passes through almost everything).
2. The Random Nature of Decay
Radioactive decay is spontaneous and random.
- Spontaneous: It isn't affected by external factors like temperature or pressure.
- Random: We cannot predict which specific nucleus will decay next or when it will happen.
Background Radiation
Even if there isn't a radioactive source in front of you, there is always background radiation. It comes from natural sources (radon gas, cosmic rays, rocks) and man-made sources (medical X-rays).
Exam Tip: In calculations, always subtract the "background count" from your readings before doing any other math!
3. The Mathematics of Radioactive Decay
Because we deal with huge numbers of atoms, we use probability to describe decay. The decay constant (\(\lambda\)) is the probability of an individual nucleus decaying per unit time.
Key Equations
1. Activity (\(A\)): This is the number of decays per second, measured in Becquerels (Bq).
\(A = \lambda N\) (where \(N\) is the number of undecayed nuclei).
Since activity is the rate of change of \(N\), we also write: \(\frac{dN}{dt} = -\lambda N\).
2. Exponential Decay: The number of nuclei decreases exponentially over time.
\(N = N_0 e^{-\lambda t}\) and \(A = A_0 e^{-\lambda t}\).
3. Half-life (\(t_{1/2}\)): This is the average time it takes for the number of undecayed nuclei (or the activity) to halve.
\(\lambda = \frac{\ln 2}{t_{1/2}}\)
Don't worry if this seems tricky at first! Just remember that \(e^{-\lambda t}\) is the "math way" of saying something disappears by a certain percentage every second. If you plot a graph of \(N\) against \(t\), it will always show a smooth downwards curve.
4. Core Practical 15: Investigating Gamma Absorption
In this practical, you investigate how the thickness of lead affects the transmission of gamma radiation.
Step-by-step:
1. Measure the background count for a few minutes and calculate the background count rate.
2. Place a gamma source at a fixed distance from a Geiger-Muller (GM) tube.
3. Measure the count rate.
4. Place lead sheets of different thicknesses between the source and the tube.
5. Subtract the background rate from each reading to get the corrected count rate.
6. Plot a graph of \(\ln(\text{Count Rate})\) against thickness. A straight line proves the relationship is exponential.
5. Binding Energy and Mass Deficit
Here is one of the coolest parts of Physics: Mass and Energy are interchangeable!
If you weigh a nucleus, it is actually lighter than the sum of its individual protons and neutrons. This "missing mass" is called the mass deficit (\(\Delta m\)).
Einstein’s Famous Equation
\(\Delta E = c^2 \Delta m\)
The mass deficit was converted into energy when the nucleus formed. This energy is the Nuclear Binding Energy—it’s the energy you would need to supply to "break" the nucleus apart into its constituents.
The Atomic Mass Unit (\(u\))
Because atoms are so tiny, using kilograms is awkward. We use the atomic mass unit (\(u\)).
\(1u = 1.66 \times 10^{-27} \text{ kg}\).
In your exams, you’ll often convert mass in \(u\) to energy in MeV (Mega-electronvolts).
Key Takeaway: Higher binding energy per nucleon means the nucleus is more stable. Iron-56 is the "gold standard" of stability.
6. Fission and Fusion
Nuclei want to be as stable as possible (reaching that peak at Iron-56 on the binding energy curve).
Nuclear Fission
Heavy nuclei (like Uranium-235) are unstable. They can split into two smaller "daughter" nuclei. Because the total mass of the products is less than the original nucleus, energy is released. This is the process used in nuclear power stations.
Nuclear Fusion
Light nuclei (like Hydrogen) can join together to form a heavier, more stable nucleus (like Helium). This releases massive amounts of energy—even more than fission!
The Challenge: To make fusion happen, you need extremely high temperatures and densities. This is because the nuclei are both positive and repel each other (electrostatic repulsion). They need enough kinetic energy to get close enough for the Strong Nuclear Force to take over. This is what happens in the cores of stars!
Did you know? Every atom of oxygen you breathe and carbon in your body was created via nuclear fusion inside a star billions of years ago!
Summary Checklist
- Can you describe \(\alpha\), \(\beta\), and \(\gamma\) properties?
- Do your nuclear equations balance on top and bottom?
- Can you use \(N = N_0 e^{-\lambda t}\) to find the remaining nuclei?
- Do you remember to subtract background radiation?
- Can you explain why fusion requires high temperatures?