Nuclear Physics: Atoms, Radiation and Half-life
Nuclear Navigator: Split the Atom 💥
Introduction
1. Introduction
A detector clicking in an empty lab, a radiation warning sign on a door, a rock that is very slightly radioactive: all of it is nuclear physics quietly at work. This is your five-minute refresh on what's inside an atom, detecting radiation, the three types of emission, radioactive decay, half-life, and staying safe. Every idea below is one mark-earning sentence away from the exam. Let's split the atom! 💥
2. Inside the Atom: A Tiny Dense Nucleus
An atom is a tiny dense nucleus of protons (charge ) and neutrons (charge ), surrounded by electrons (charge ) orbiting far outside. Almost all the mass sits in the nucleus; almost all the volume is empty space. The positive nucleus attracts the negative electrons, which keeps them in orbit. A neutral atom has equal protons and electrons, so the charges cancel. An atom that loses electrons becomes a positive ion; one that gains electrons becomes a negative ion. Only the electrons change: the nucleus, and so the element, stays the same.
Key idea🔑 Key idea: Atom = tiny dense positive nucleus (protons + neutrons) + orbiting electrons, mostly empty space. Lose electrons → positive ion; gain electrons → negative ion.
Worked example
Worked Example: From Atom to Ion
Worked Example: Lose One, Gain a Charge 🎯
A sodium atom has protons and electrons. It loses one electron. State the charge on the particle formed, and whether it is still sodium.
- 1Charges: , so it is a positive ion with charge . The nucleus has not changed, so it still has protons and is still sodium: ions form by losing or gaining electrons, never protons.
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3. The Nucleus, Isotopes and Nuclide Notation
The nucleus holds protons and neutrons, together called nucleons. We label any nuclide as : the bottom number is the proton number (it fixes which element you have), the top number is the nucleon number (protons + neutrons). The number of neutrons is always . Isotopes are atoms of the same element (same ) with different numbers of neutrons (different ). They are the same element because the element depends only on the number of protons; the extra neutrons make the nucleus heavier but do not change its charge. Some isotopes are stable and some are radioactive: carbon-12 is stable, carbon-14 is radioactive.
Key idea🔑 Key formula: → protons (bottom), neutrons . Same , different = isotopes.
Worked example
Worked Example: Reading a Nuclide
Worked Example: Counting the Particles 🧮
For , state the number of protons, neutrons, and electrons (neutral atom).
- 1Protons . Neutrons . Neutral atom, so electrons protons .
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4. Detecting Radioactivity and Background
Some nuclei are unstable and emit radiation; we detect it with a Geiger-Müller tube and counter, which records a count rate. But the detector clicks even with no source nearby: that's background radiation, around us all the time. The main sources are radon gas in the air, rocks and buildings, food and drink, and cosmic rays, with a small artificial part (mainly medical X-rays and scans). The counter gives a count rate: , in counts/s or counts/minute.
Key idea🔑 Key idea: Count rate = counts ÷ time. Background radiation is always present: radon gas, rocks and buildings, food and drink, cosmic rays.
Worked example
Worked Example: Calculating a Count Rate
Worked Example: The Honest Count 🔍
A GM tube and counter, with no radioactive source anywhere near, record counts in minutes. Find the count rate in counts/minute and in counts/s, and explain why it is not zero.
- 1counts/minute. A minute is s, so counts/s. It is not zero because of background radiation, which is around us all the time.
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5. Alpha, Beta and Gamma: Know Your Radiation
Unstable nuclei emit three kinds of radiation. Alpha () is a helium nucleus (2 protons + 2 neutrons, charge ): the most ionising, the least penetrating (stopped by paper or skin). Beta () is a fast electron (charge ): medium ionising, stopped by a few mm of aluminium. Gamma () is a high-energy electromagnetic wave (no charge, no mass): the least ionising, the most penetrating (only reduced by thick lead or concrete). The pattern: more ionising means less penetrating. Emission is spontaneous and random in direction, so radiation goes out all around a source.
Key idea🔑 Key idea: α = He nucleus (most ionising, stopped by paper); β = fast electron (stopped by aluminium); γ = EM wave (stopped only by thick lead). More ionising → less penetrating.
Worked example
Worked Example: Identifying Radiation by Absorption
Worked Example: What Gets Through? 🧱
A source's count rate is unchanged by paper, drops sharply when a few mm of aluminium is added, and the rest only fades behind thick lead. Which radiations are present?
- 1Paper makes no difference → no alpha (paper would stop alpha). So beta and/or gamma.
- 2Aluminium cuts the count → beta is present (a few mm of aluminium stops beta).
- 3Radiation still gets through the aluminium and only thick lead reduces it → gamma is present too (only gamma penetrates aluminium and needs lead).
- 4Conclusion: the source emits beta and gamma, no alpha. The trick is always to add absorbers in order (paper → aluminium → lead) and watch where the count drops.
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6. Radioactive Decay
Radioactive decay is spontaneous (happens on its own) and random (you can't predict which nucleus goes next), and nothing you do to the source (heating, cooling, crushing, chemistry) changes it. Decay is a change in an unstable nucleus that gives out alpha or beta particles and/or gamma radiation. The element depends on the number of protons, so: in alpha decay the alpha particle carries away protons and the nucleus becomes a different element; in beta decay the proton number changes, so again it becomes a different element; gamma has no charge and no mass, so gamma alone leaves the same element. For example, radium-226 gives out an alpha particle and becomes radon; carbon-14 gives out a beta particle and becomes nitrogen-14.
Key idea🔑 Key idea: Decay is spontaneous and random. Alpha or beta → a different element; gamma alone → the same element.
Worked example
Worked Example: Same Element After Decay?
Worked Example: Who Changes Element? ⚛️
(a) A radium-226 nucleus, , emits an alpha particle. (b) A carbon-14 nucleus, , emits a beta particle. (c) Another nucleus emits only gamma radiation. For each, state whether the nucleus left behind is the same element, and why.
- 1(a) Different element (radon): the alpha particle carries away protons, so the proton number changes.
- 2(b) Different element (nitrogen): in beta decay the proton number changes. (c) Same element: gamma has no charge and no mass and only carries away energy, so the number of protons is unchanged.
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7. Half-life: The Steady Halving
Because decay is random, you can't time a single nucleus, but across billions the same fraction decays in equal times. The half-life is the time for half the unstable nuclei (or for the activity/count rate) to decay. After half-life, half is left; after , a quarter; after , an eighth: the fraction remaining after half-lives is . The amount keeps halving but never reaches zero. Half-life is fixed by the isotope alone, unaffected by temperature, pressure, chemistry, or how much you have.
Key idea🔑 Key formula: Fraction left after half-lives . Count the halvings; half-life is fixed by the isotope and never reaches zero.
Worked example
Worked Example: Fraction Remaining After N Half-lives
Worked Example: Keep Halving ✂️
An isotope has a half-life of years. A sample starts with g. How much remains after years?
- 1Number of half-lives: .
- 2Halve the mass three times: g. (Same as .)
- 3g remains after years. Check: three halvings leave an eighth, and g ✓. For a decay-curve version, count the halvings between the start and end activities to get , then half-life .
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8. Radiation Safety
Ionising radiation knocks electrons off atoms in living cells, which can cause cell death, mutations (damage to DNA) and cancer, sometimes years later. Store sources in locked, lead-lined boxes; carry a source in its box; pick it up with long-handled tongs at arm's length, never bare hands; never point it at anyone; keep it out of its box for as short a time as possible; and wear a film badge if you work with radiation. Danger depends on where the source is: outside the body gamma is the bigger hazard (it penetrates deep, while alpha can't get past your skin), but inside the body alpha is the most dangerous because it's the most strongly ionising. The picture shows these actions: a lead-lined store, tongs, a film badge, a source pointed away, a clock for keeping the time short, and a lead barrier.
Key idea🔑 Key idea: Radiation causes cell death, mutations and cancer. Locked lead-lined store, tongs at arm's length, never point it at people, out for the shortest time. Outside the body gamma is worst; inside, alpha is worst.
Worked example
Worked Example: Handling a Source Safely
Worked Example: Three Precautions 🧤
State three precautions for moving a radioactive source from the store room to a lab and using it, and why each helps.
- 1Carry it in its lead-lined box by the shortest route, because lead absorbs the radiation. Lift it with long-handled tongs at arm's length, so it is never in your hand. Never point it at anyone, and put it back in its box as soon as you have finished. A film badge tracks how much radiation a worker has received.
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