Describe the evidence for the nuclear atom, represent nuclides and isotopes, and balance nuclear reaction and decay equations

What this dot point is asking

SEAB wants you to describe the experimental evidence for the nuclear model of the atom, to represent nuclides and isotopes in standard notation, and to balance nuclear reaction and decay equations by conserving nucleon and proton numbers. This frames the structure of matter that the rest of nuclear physics builds on.

The answer

Evidence for the nuclear atom

The alpha-scattering experiment fired alpha particles at a thin gold foil. Two observations were decisive:

• Most alpha particles passed straight through with little or no deflection, showing that the atom is mostly empty space.
• A very small fraction were deflected through large angles, some bouncing almost straight back, showing that the positive charge and nearly all the mass are concentrated in a tiny, dense region.

These results overturned the earlier "plum pudding" picture and established the nuclear model: a small, dense, positively charged nucleus surrounded by electrons, with most of the atom empty.

Nuclide notation

A nuclide is a specific nuclear species, written:

where $X$ is the chemical symbol, $Z$ is the proton (atomic) number (the number of protons, which fixes the element), and $A$ is the nucleon (mass) number (the total number of protons and neutrons). The number of neutrons is $A - Z$.

Isotopes

Isotopes of an element have the same proton number $Z$ but different nucleon numbers $A$, that is, the same number of protons but different numbers of neutrons. They are chemically identical but differ in mass and may differ in nuclear stability. Carbon-12 and carbon-14 are isotopes of carbon.

Radioactive emissions

Unstable nuclei emit radiation to become more stable:

• Alpha ($\alpha$): a helium nucleus $^4_2\text{He}$; reduces $A$ by $4$ and $Z$ by $2$.
• Beta-minus ($\beta^-$): an electron $^{\ \ 0}_{-1}\text{e}$ emitted when a neutron becomes a proton; $A$ unchanged, $Z$ increases by $1$.
• Gamma ($\gamma$): a high-energy photon; no change in $A$ or $Z$, just a loss of excess energy.

Balancing nuclear equations

In any nuclear reaction or decay, two quantities are conserved:

• the total nucleon number $A$ (the top numbers balance),
• the total proton number $Z$ (the bottom numbers balance, conserving charge).

Use these two conservation rules to identify an unknown product.

Examples in context

Example 1. Smoke detectors. A common smoke detector contains a tiny americium source that emits alpha particles, ionising the air in a chamber and allowing a small current to flow. Smoke disrupts this current, triggering the alarm. The alpha emitter is chosen because alpha particles are easily stopped and stay safely inside the device.

Example 2. Decay chains. A heavy nucleus like uranium-238 decays through a long series of alpha and beta emissions, each step balanced by conserving nucleon and proton numbers, until it reaches stable lead-206. Tracking the chain is just repeated application of the two conservation rules.

Try this

Q1. State the two key observations of the alpha-scattering experiment and what each shows. [2 marks]

• Cue. Most pass straight through (atom mostly empty space); a few deflect sharply (small, dense, positive nucleus).

Q2. Write the nuclide notation for an isotope of oxygen with $8$ protons and $10$ neutrons. [1 mark]

• Cue. $^{18}_{8}\text{O}$ (nucleon number $8 + 10 = 18$).

Q3. A polonium-210 nucleus ($^{210}_{84}\text{Po}$) emits an alpha particle. Identify the daughter nucleus by its nucleon and proton numbers. [2 marks]

• Cue. Nucleon number $210 - 4 = 206$; proton number $84 - 2 = 82$ (lead), giving $^{206}_{82}\text{Pb}$.