Welcome to the World of Radioactivity!
This chapter dives into the fascinating, microscopic world of the nucleus. We will explore why some atoms are unstable, how they decay, and what kind of radiation they emit. Don't worry if this seems tricky at first; radioactivity governs everything from medical imaging to generating power, so understanding these core concepts is incredibly important!
3.3.3 The Basics of Radioactive Decay
What Makes a Nucleus Unstable?
An atom is radioactive if its nucleus is unstable. Unstable nuclei emit particles or electromagnetic waves to try and reach a lower, more stable energy state. This emission process is called radioactive decay.
Two fundamental characteristics govern decay:
- Spontaneous: Decay happens randomly, unaffected by external factors like temperature, pressure, or chemical bonding. You cannot predict when a specific nucleus will decay.
- Random: We can only state the probability that a nucleus will decay in a given time, not certainty.
Quick Review: Nuclide Notation (\( {}^{A}_{Z}X \))
To write decay equations, you must remember nuclide notation:
- A: Nucleon Number (Mass Number = Protons + Neutrons)
- Z: Proton Number (Atomic Number = Protons)
- X: Chemical Symbol
During any decay process, both the total nucleon number (A) and the total proton number (Z) must be conserved (stay the same) across the equation.
The Three Main Decay Modes: \(\alpha\), \(\beta\), and \(\gamma\)
Radioactive nuclei typically decay via three major types of emission. Their differences lie in their composition, charge, penetrating power, and ability to ionise.
1. Alpha (\(\alpha\)) Radiation
- Nature: A fast-moving helium nucleus (\( {}^{4}_{2}\text{He} \)).
- Charge: +2e (Positive).
- Mass: Relatively heavy (4 atomic mass units).
- Ionisation Power: Very High. Because they are heavy and highly charged, they easily strip electrons from atoms they pass, making them dangerous internally.
- Penetrating Power: Very Low. Stopped easily by a thin sheet of paper or a few centimetres of air. (Analogy: Like a slow, heavy bowling ball.)
2. Beta Minus (\(\beta^-\)) Radiation
- Nature: A fast-moving electron (\( {}^{0}_{-1}e \)).
- Charge: -1e (Negative).
- Mass: Very light.
- Ionisation Power: Medium. Less charged and much lighter than alpha, so it interacts less frequently.
- Penetrating Power: Medium. Stopped by a few millimetres of aluminium or plastic.
3. Gamma (\(\gamma\)) Radiation
- Nature: High-energy photon (an electromagnetic wave).
- Charge: Zero (Neutral).
- Mass: Zero (just energy).
- Ionisation Power: Very Low. Since they are uncharged, they interact with matter less often.
- Penetrating Power: Very High. Requires thick lead or many metres of concrete to significantly stop them. (Analogy: Like light, but with immense energy.)
Key Takeaway: Alpha, Beta, Gamma
The relationship between ionisation and penetration is an inverse one:
High Ionisation (\(\alpha\)) means Low Penetration.
Low Ionisation (\(\gamma\)) means High Penetration.
3.3.3 Decay Equations and Particle Conservation
Alpha Decay (\(\alpha\))
This occurs in very heavy, proton-rich nuclei. The nucleus sheds 2 protons and 2 neutrons.
Rule: Z decreases by 2, A decreases by 4.
Example: Uranium-238 decaying into Thorium-234:
\[
{}^{238}_{92}\text{U} \rightarrow {}^{234}_{90}\text{Th} + {}^{4}_{2}\alpha
\]
Check: Total A on left (238) = Total A on right (234 + 4). Total Z on left (92) = Total Z on right (90 + 2). Conservation achieved!
Beta Minus Decay (\(\beta^-\))
This occurs in neutron-rich nuclei. A neutron inside the nucleus converts into a proton, an electron (the \(\beta^-\) particle), and an antineutrino (\(\bar{\nu}\)).
\[
{}^{1}_{0}n \rightarrow {}^{1}_{1}p + {}^{0}_{-1}e + \bar{\nu}
\]
Rule: Z increases by 1, A stays the same.
Example: Carbon-14 decaying into Nitrogen-14:
\[
{}^{14}_{6}\text{C} \rightarrow {}^{14}_{7}\text{N} + {}^{0}_{-1}\beta^- + \bar{\nu}
\]
Did you know? The Neutrino Hypothesis
The existence of the neutrino or antineutrino (\(\nu\) or \(\bar{\nu}\)) was hypothesised to ensure the fundamental physics laws were conserved: energy and momentum. In beta decay, the energy of the emitted electrons seemed variable, suggesting a tiny, neutral, undetectable particle was also sharing the energy—this particle was the neutrino (or antineutrino, specifically for \(\beta^-\) decay).
Note: The decay of a free neutron (as shown above: \(n \rightarrow p + e^- + \bar{\nu}\)) is an important process to know.
Beta Plus Decay (\(\beta^+\))
This occurs in proton-rich nuclei. A proton inside the nucleus converts into a neutron, a positron (the \(\beta^+\) particle, which is the electron's antiparticle), and a neutrino (\(\nu\)).
\[
{}^{1}_{1}p \rightarrow {}^{1}_{0}n + {}^{0}_{1}e^+ + \nu
\]
Rule: Z decreases by 1, A stays the same.
Example: Fluorine-18 decaying into Oxygen-18:
\[
{}^{18}_{9}\text{F} \rightarrow {}^{18}_{8}\text{O} + {}^{0}_{1}\beta^+ + \nu
\]
Gamma Emission (\(\gamma\))
Gamma radiation is pure energy. It typically occurs after an alpha or beta decay leaves the daughter nucleus in an excited state (like an atom whose electrons are excited). The nucleus drops down to a stable energy state by releasing a gamma ray photon.
Rule: Z and A both stay the same.
Example: Technetium-99m (\(m\) stands for metastable, meaning excited) decaying to Technetium-99:
\[
{}^{99m}_{43}\text{Tc} \rightarrow {}^{99}_{43}\text{Tc} + \gamma
\]
Technetium-99m is widely used in medical diagnosis because it emits easily detectable gamma rays but has a short half-life, limiting patient exposure.
QUICK REVIEW: What is conserved in all decays?
1. Nucleon Number (A)
2. Proton Number (Z) (Charge)
3. Momentum and Energy (thanks to the neutrino/antineutrino!)
Half-Life and Activity
Half-Life (\(T_{1/2}\))
Since radioactive decay is random, we describe the speed of the decay process using half-life.
Definition: The half-life (\(T_{1/2}\)) is the time taken for the number of unstable nuclei (N) in a sample to halve, or, equally, the time taken for the activity (A) of the sample to halve.
Activity (A): This is the rate of decay, measured in Becquerels (Bq), where 1 Bq means 1 decay per second. Activity is directly proportional to the number of unstable nuclei remaining.
Simple Half-Life Calculations (AS Level Requirement)
For AS, you only need to perform simple calculations involving times that are whole numbers of the half-life.
Analogy: Imagine you start with $100. If the half-life for losing half your money is 1 hour:
If a source has an initial activity of 800 Bq and a half-life of 2 hours, after 4 hours (2 half-lives), the activity will be \(800 \rightarrow 400 \rightarrow 200\) Bq.
Determining Half-Life Graphically
The half-life can be found directly from a graph of count rate (or activity) against time.
Step 1: Start with the initial activity/count rate \(A_0\).
Step 2: Find the time taken for the activity to drop to \(A_0/2\). This time is \(T_{1/2}\).
Step 3: Check your result by finding the time taken for the activity to drop from \(A_0/2\) to \(A_0/4\). This time should also equal \(T_{1/2}\).
Important Note on A2 Content: While we rely on graphical and simple methods here, at A2 level, you will use the full exponential decay equations like \(N = N_0 e^{-\lambda t}\) and \(T_{1/2} = \ln 2 / \lambda\) for more complex calculations. For now, focus on the definitions and graphical interpretation!
Radiation Hazards, Applications, and Safety
Relative Hazards of Radiation
The danger posed by a radioactive source depends entirely on where the radiation is delivered (internal or external) and its properties (penetration and ionisation).
- External Exposure:
- \(\alpha\): Low hazard, as it cannot penetrate the skin (dead layer of cells).
- \(\beta\): Medium hazard, can penetrate skin and cause burns/damage.
- \(\gamma\): High hazard, as it penetrates deep into the body, damaging internal organs throughout the body.
- Internal Exposure (if ingested or inhaled):
- \(\alpha\): Extreme hazard. While inside, it deposits all its high ionisation energy directly into soft tissue, causing severe local damage.
- \(\beta\): Medium hazard, localized damage.
- \(\gamma\): Low hazard (the rays pass straight through, mostly escaping the body).
Radiation Safety and Handling
The three pillars of radiation safety are:
1. Time: Minimise the time spent near the source.
2. Distance: Maximise the distance from the source.
3. Shielding: Use appropriate materials (paper for \(\alpha\), aluminium for \(\beta\), lead/concrete for \(\gamma\)).
Inverse-Square Law for Gamma Radiation
When dealing with a point source, the intensity (\(I\)) of the radiation detected follows the inverse-square law:
\[
I \propto \frac{1}{r^2}
\]
Where \(r\) is the distance from the source.
This means if you double the distance, the intensity drops to one quarter (1/4). This is a crucial principle for radiation safety (distance is your friend!) and applies mainly to gamma radiation because it is so penetrating it acts like a ray of light originating from a point.
Background Radiation and Elimination
Radioactivity is naturally present all around us. Background radiation comes from several sources:
- Cosmic rays (high-energy particles from space).
- Terrestrial sources (radioactive rocks and soil, especially Radon gas).
- Man-made sources (medical procedures, nuclear testing fallout).
When conducting experiments in the lab, you must account for this background radiation. To eliminate background radiation from calculations:
Step 1: Measure the count rate of the environment with the source removed (the background count rate).
Step 2: Subtract the background count rate from all subsequent measurements taken with the source present. This gives the corrected count rate (Activity, A) solely due to the radioactive source being investigated.
Applications of Radioactivity
Radioactive sources are used widely, taking advantage of their penetrating properties:
- Thickness Gauging:
- \(\beta\) sources are used to monitor the thickness of thin materials like paper or aluminium foil. If the sheet gets too thick, the count rate drops, triggering a response.
- \(\gamma\) sources are used for thicker materials like steel plate, as they require high penetration.
- Medical Diagnosis: As mentioned, technetium-99m is used as a radioactive tracer because it emits gamma radiation (easily detectable outside the body) and has a short half-life.
Chapter Summary: Key Takeaways
1. Conservation: Nucleon number (A) and proton number (Z) must balance in all decay equations.
2. Properties: \(\alpha\) is high ionising/low penetrating. \(\gamma\) is low ionising/high penetrating.
3. Beta Decay: \(\beta^-\) creates an antineutrino and increases Z by 1. \(\beta^+\) creates a neutrino and decreases Z by 1. Neutrinos ensure energy and momentum conservation.
4. Half-life (\(T_{1/2}\)): Time for activity or number of nuclei to halve. Used for simple whole-number calculations and graphical analysis.
5. Safety: Use shielding, distance (\(I \propto 1/r^2\) for \(\gamma\)), and minimise time. Always subtract background radiation from experimental counts.