Nuclear Physics & Radioactivity

1. The Structure of the Atom & Nucleus

At the heart of every atom lies the nucleus, a dense core containing positively charged protons and neutral neutrons. Collectively, protons and neutrons are known as nucleons. Orbiting the nucleus are negatively charged electrons.

Key definitions for describing a nucleus:

• Proton Number (Z): Also known as the atomic number, this is the number of protons in a nucleus. It defines the chemical element.
• Nucleon Number (A): Also known as the mass number, this is the total number of protons and neutrons in the nucleus (A = Z + number of neutrons).

We represent a specific nucleus (a nuclide) using the notation:

`^A_Z X`

Where X is the chemical symbol, A is the nucleon number, and Z is the proton number. For example, a standard carbon atom is `¹²₆C`, meaning it has 6 protons and (12 - 6) = 6 neutrons.

Isotopes are atoms of the same element that have the same number of protons (same Z) but a different number of neutrons (different A). For instance, Carbon-14 (`¹⁴₆C`) is an isotope of Carbon-12 (`¹²₆C`). It has 6 protons but 8 neutrons. Since they have the same number of electrons, isotopes have identical chemical properties but different nuclear stability.

2. Radioactivity: The Unstable Nucleus

Some isotopes have an unstable combination of protons and neutrons. To achieve stability, their nuclei spontaneously disintegrate, emitting energy in the form of particles or electromagnetic waves. This process is called radioactive decay, and such isotopes are known as radioisotopes.

Two crucial characteristics of radioactive decay are:

1. Spontaneous: The decay process is not influenced by external physical or chemical conditions like temperature, pressure, or chemical reactions.
2. Random: It is impossible to predict when a particular nucleus will decay. We can only talk about the probability of decay over time for a large number of nuclei.

The emissions from radioactive decay are called ionising radiation because they have enough energy to knock electrons out of atoms they collide with, creating ions.

3. Types of Ionising Radiation

There are three main types of radiation emitted from unstable nuclei:

| Property | Alpha (α) Particle | Beta (β) Particle | Gamma (γ) Ray |

| ------------------ | ---------------------------------- | ---------------------------------- | ------------------------------------ |

| Nature | Helium nucleus (2 protons, 2 neutrons) | High-speed electron | High-frequency electromagnetic wave |

| Symbol | `⁴₂He` or `α` | `⁰₋₁e` or `β` | `γ` |

| Charge | +2e (doubly positive) | -1e (negative) | 0 (neutral) |

| Penetrating Power| Low (stopped by paper or a few cm of air) | Medium (stopped by ~5mm of aluminium) | High (stopped by several cm of lead) |

| Ionising Effect | Very high (due to large mass and charge) | Medium | Low |

Common Misconception: The electron in beta decay originates from the nucleus itself when a neutron transforms into a proton and an electron (`n → p + e⁻`), not from the electron shells.

4. Radioactive Decay and Half-Life

Radioactive Decay Equations

When a nucleus decays, both the nucleon number (A) and proton number (Z) must be conserved.

• Alpha Decay: The nucleus loses 2 protons and 2 neutrons. `^A_Z X → ^(A-4)_(Z-2) Y + ⁴₂He`
• Beta Decay: A neutron turns into a proton, and an electron is emitted. `^A_Z X → ^A_(Z+1) Y + ⁰₋₁e`
• Gamma Decay: An excited nucleus releases energy as a gamma ray to become more stable. A and Z do not change. This often follows alpha or beta decay.

Half-Life (t½)

The half-life is the average time taken for half of the unstable nuclei in a radioactive sample to decay, or for the activity of the sample to halve. Activity is the rate of decay, measured in Becquerels (Bq), where 1 Bq = 1 decay per second.

Example Calculation:

A sample of Iodine-131 has a half-life of 8 days. If its initial activity is 1200 Bq, what is its activity after 24 days?

1. Calculate the number of half-lives: 24 days / 8 days = 3 half-lives.
2. Calculate the final activity:

• After 1st half-life (8 days): 1200 / 2 = 600 Bq
• After 2nd half-life (16 days): 600 / 2 = 300 Bq
• After 3rd half-life (24 days): 300 / 2 = 150 Bq

The final activity is 150 Bq.

Exam Tip: In experiments measuring half-life, you must first measure the **background radiation** (from sources like cosmic rays and rocks) and subtract this value from all your readings before plotting a decay curve.

5. Nuclear Fission and Fusion

Nuclear Fission

Nuclear fission is the process where a large, unstable nucleus (like Uranium-235) splits into two smaller nuclei, releasing a huge amount of energy and 2-3 additional neutrons.

The process: `¹₀n + ²³⁵₉₂U → ²³⁶₉₂U (unstable) → Ba + Kr + 3(¹₀n) + Energy`

If the released neutrons strike other U-235 nuclei, they can cause further fissions, leading to a chain reaction. In nuclear power plants, like the Chashma Nuclear Power Plant in Punjab, this reaction is controlled using control rods (to absorb excess neutrons) and a moderator (to slow down neutrons) to generate electricity safely.

Nuclear Fusion

Nuclear fusion is the process where two light nuclei combine (or fuse) to form a single, heavier nucleus, releasing even more energy per nucleon than fission. This is the process that powers the Sun and other stars.

Example: `²₁H (Deuterium) + ³₁H (Tritium) → ⁴₂He + ¹₀n + Energy`

Fusion requires extremely high temperatures and pressures to overcome the electrostatic repulsion between the positive nuclei. Replicating and sustaining these conditions on Earth for power generation remains a major scientific challenge.

6. Applications and Safety

Ionising radiation has many beneficial uses but must be handled with care due to its health risks (cell damage, cancer).

• Medical: Sterilising surgical instruments (gamma), radiotherapy for cancer (Cobalt-60), and as tracers for diagnosis (Technetium-99m).
• Industrial: Smoke detectors (Americium-241), checking welds, and measuring material thickness (beta radiation).

Safety Precautions are essential:

• Minimise exposure time.
• Maximise distance from the source.
• Use appropriate shielding (e.g., lead aprons, concrete walls).