• Background radiation is always around us — from natural sources (radon gas, cosmic rays, food) and man-made sources (medical, nuclear waste, fallout). You must subtract it to get the corrected count rate.
• Alpha (α) = 2p + 2n (helium nucleus), Beta (β⁻) = high-energy electron, Gamma (γ) = electromagnetic wave — each has different mass, charge, penetration and ionising power.
• Nuclear decay equations must balance — mass number (top) and atomic/proton number (bottom) balance on both sides, just like a chemical equation.
• Core Practical 15 investigates how lead thickness absorbs gamma radiation — count rate falls until it reaches background level.
• Radioactive decay is random (can't predict which nucleus decays when) and spontaneous (unaffected by temperature, pressure, chemical conditions).
• Activity A = ΔN/Δt = −λN — the decay constant λ is the probability per second that one nucleus decays.
• Decay follows an exponential pattern: N = N₀e^(−λt), and the number of nuclei never actually reaches zero.
• Half-life t½ is the time for half the nuclei (and half the activity) to decay: t½ = ln2 / λ.

Background radiation is low-level radiation from environmental sources that is always present around us, whether or not you're doing an experiment. It's measured in counts per second, in a unit called the Becquerel (Bq).

Think of it like background noise in a room — even in "silence," there's always a faint hum. In radioactivity, that hum comes from two broad categories of sources:

This is the trick examiners love to test: to find the true activity of a source, you measure the count rate with no source present (this is your background rate), then measure the count rate with the source present, and subtract:

How to spot it on a graph: if a count-rate-vs-time (or vs-distance) graph seems to level off at some value above zero instead of dropping to zero, that flat value is the background radiation — not evidence that the source is still emitting strongly!

Some nuclei are unstable — usually because the ratio of protons to neutrons isn't balanced right, or the nucleus is simply too big. To become more stable, the nucleus needs to shed some mass, charge, or energy. It does this by emitting one of three things: an alpha particle, a beta particle, or a gamma ray. This is called radioactive decay.

Alpha particles are emitted from nuclei that are too large. Since an alpha particle is identical to a helium nucleus, this is written as ⁴₂α or ⁴₂He. Because it's big, heavy, and doubly-charged, alpha is strongly ionising but weakly penetrating — stopped by a sheet of paper or a few cm of air.

Beta-minus particles are emitted from nuclei with too many neutrons — one neutron essentially converts into a proton and spits out a fast electron. Beta is moderately ionising and moderately penetrating — travels 20 cm to 3 m in air, and is stopped by a few mm of aluminium.

Gamma rays are emitted when a nucleus has excess energy but doesn't need to change its proton/neutron numbers — it's pure electromagnetic radiation escaping the nucleus. Gamma is weakly ionising but very highly penetrating — you need thick lead or several metres of concrete to significantly absorb it.

Just like balancing a chemical equation, nuclear equations must balance on both the top numbers (mass/nucleon number) and the bottom numbers (atomic/proton number).

Why does beta emission increase the proton number? A beta-minus particle is an electron created when a neutron inside the nucleus converts into a proton (plus the electron, which is ejected). So the nucleus loses a neutron but gains a proton — mass number (protons + neutrons) is unchanged, but proton number goes up by 1.

Consider ²³⁷₉₂W undergoing three decays in sequence: β⁻, then α, then β⁺.

Step 1 — β⁻ decay: nucleon number stays the same (237), proton number increases by 1 (92 → 93). Result: ²³⁷₉₃X

Step 2 — α decay: nucleon number drops by 4 (237 → 233), proton number drops by 2 (93 → 91). Result: ²³³₉₁Y

Step 3 — β⁺ decay: nucleon number stays the same (233), proton number decreases by 1 (91 → 90, since a positron is emitted when a proton converts to a neutron). Result: ²³³₉₀Z

Aim: investigate how the thickness of lead affects the absorption of gamma rays.

Method (simplified):

1. Measure background radiation with no source present, over 5 minutes, and find the average per minute.
2. Measure the thickness of each lead sheet with Vernier calipers at 3 points, and average.
3. Place the source a fixed 10 cm from the GM tube, record count rate over 1 minute, and repeat 3 times.
4. Insert the thinnest lead absorber and repeat the readings.
5. Repeat with increasingly thick lead sheets, taking 3 readings at each thickness.

Systematic errors: keep the source stored well away from the counter when not testing (or it'll skew "background" readings), and always run the whole experiment in the same location (background radiation levels vary by location).

Random errors: improve reliability by using a source with a long half-life and activity well above background level, so natural random fluctuations don't dominate your readings.

Safety: store the source in a lead-lined container when not in use, keep about a metre of distance from it during use, always handle it with tongs pointing away from you, and wash your hands afterwards.

Radioactive decay is the spontaneous disintegration of a nucleus to form a more stable one, releasing an alpha, beta, or gamma particle. If you point a GM tube at a radioactive source, the individual clicks are irregular — you genuinely cannot predict exactly when the next click will happen. This irregularity is the direct evidence for the randomness of decay.

Two important formal definitions here — these get asked as exam questions almost every year:

Here's the beautiful part: even though you can't predict a single nucleus, with billions upon billions of nuclei in a real sample, the statistics smooth out into a completely predictable curve for the group as a whole. This is exactly like flipping one coin (unpredictable) versus flipping a million coins (you can predict very confidently that ~50% will land heads).

Since we can't track individual decays, physicists instead assign every radioactive isotope a decay constant λ — a fixed number describing how "eager" that isotope is to decay.

A large λ means each nucleus is very likely to decay in the next second — a highly unstable, "hot" isotope. A small λ means it's much more patient.

In plain words: the more radioactive nuclei you still have left (N), and the "twitchier" they are (λ), the higher the activity. The minus sign just reminds us N is decreasing over time — for calculations, you can usually drop it and just take magnitudes.

Because activity depends on how many nuclei are left (A = λN), and the number of nuclei is constantly falling, the whole system feeds back on itself — fewer nuclei means a lower activity, which means fewer decays per second, which means the number falls even more slowly. This self-referencing decrease is exactly what produces an exponential curve: steep at first, then flattening out, but mathematically never quite reaching zero.

The exact same shape of equation applies to activity and count rate too, since both are directly proportional to N:

Reading the graph: A steeper initial slope means a larger λ (faster decay, shorter half-life). A shallow, lazy slope means a smaller λ (slower decay, longer half-life).

You can derive the half-life formula by substituting N = ½N₀ at t = t½ into the decay equation and solving for t½ using natural logs:

This is arguably the single most important relationship in this whole chapter, because it lets you flip between "how fast is this decaying" (λ, a probability) and "how long until half is gone" (t½, an actual time you can picture and measure).