The nuclear atom
| English | Chinese | Pinyin |
|---|---|---|
| nucleus | 原子核 | yuán zǐ hé |
| protons | 质子 | zhì zi |
| neutrons | 中子 | zhōng zi |
| nuclide | 核素 | hé sù |
| proton number | 质子数 | zhì zi shù |
| nucleon number | 核子数 | hé zǐ shù |
| nucleons | 核子 | hé zǐ |
| isotopes | 同位素 | tóng wèi sù |
| atomic mass unit | 原子质量单位 | yuán zi zhì liàng dān wèi |
Firing at gold foil
- Rutherford's team fired α-particles at a thin gold foil.
- Most went straight through — but a rare few bounced almost straight back.
- "As if you fired a shell at tissue paper and it came back at you."
Nuclear atom evidence lab
Connect observations to the nuclear model of the atom.
What the scattering showed
- Most pass through → the atom is mostly empty space.
- A rare big deflection → a tiny, dense, positive nucleus 原子核 holds the charge and mass.
Most alpha-particles pass nearly straight through; a few are deflected sharply by the tiny nucleus
Most α-particles passing straight through the gold foil showed that the atom is:
If most go straight through, there is little in the way — the atom is mostly empty, with the mass and charge concentrated in a tiny nucleus.
The nuclear model
- Nucleus: protons 质子 (charge $+e$) and neutrons 中子 (no charge). Electrons ($-e$) surround it.
- The atom is $\sim 10^{-10}\ \text{m}$; the nucleus only $\sim 10^{-15}\ \text{m}$ — but holds nearly all the mass.
- A neutral atom has as many electrons as protons.
Simple models of a helium atom and a lithium atom (not to scale)
Almost all of an atom's mass is in its nucleus.
Protons and neutrons are ~1 u each; electrons are ~1/1836 u, so the nucleus holds nearly all the mass.
Notation
- A nuclide 核素 is written $^{A}_{Z}\text{X}$: $Z$ = proton number 质子数 (fixes the element), $A$ = nucleon number 核子数.
- Number of neutrons $N = A - Z$. Protons and neutrons together are nucleons 核子.
Protons and neutrons together are called ____.
The nucleon number $A$ counts the protons plus neutrons in the nucleus.
How many neutrons are in $^{14}_{6}\text{C}$?
$N = A - Z = 14 - 6 = 8$ neutrons.
Isotopes 同位素
- Isotopes have the same proton number $Z$ but different numbers of neutrons.
- Example: $^{12}_{6}\text{C}$ and $^{14}_{6}\text{C}$ — same element, different mass.
Nuclide notation: nucleon number on top, proton number below
Isotopes of an element have:
Same $Z$ (so same element and chemistry) but different $N$, giving a different mass number $A$.
What's conserved
- In any nuclear process, nucleon number $A$ and charge are conserved.
- These two rules let you balance every decay equation: the top numbers must add up on both sides, and so must the bottom numbers.
In a nuclear process, which quantities are always conserved?
Nucleon number and charge are conserved. Proton and neutron numbers can each change (e.g. in β-decay a neutron becomes a proton).
Match each emitted particle to how it is written in a decay equation.
The top number is the nucleon number and the bottom the charge; both must balance across the equation.
Worked example: tritium
Tritium, $^{3}_{1}\text{H}$, is a radioactive isotope of hydrogen that emits a β$^{-}$ particle.
- Particles in a neutral atom: $Z = 1$ proton; $N = 3 - 1 = 2$ neutrons; $1$ electron (equal to the protons).
- Decay equation: $^{3}_{1}\text{H} \to {}^{3}_{2}\text{He} + {}^{0}_{-1}\beta + \bar{\nu}$. Check: top $3 = 3 + 0$; bottom $1 = 2 + (-1)$. The extra particle is an antineutrino.
- Quarks in the nucleus: a proton is uud and a neutron is udd, so one proton and two neutrons contain $2 + 1 + 1 = 4$ up quarks and $1 + 2 + 2 = 5$ down quarks.
- Check the charge: $4\left(+\tfrac{2}{3}\right) + 5\left(-\tfrac{1}{3}\right) = \tfrac{8}{3} - \tfrac{5}{3} = +1$, the charge of the single proton.
Worked example: a chain of decays
A nucleus of radium-228, $^{228}_{88}\text{Ra}$, decays through a series of steps in which five α-particles and four β$^{-}$ particles are emitted. Identify the final nucleus.
- Nucleon number: each α removes $4$, each β$^{-}$ removes none: $A = 228 - 5 \times 4 = 208$.
- Proton number: each α removes $2$, each β$^{-}$ adds $1$: $Z = 88 - 10 + 4 = 82$.
- Answer: $^{208}_{82}\text{Pb}$ — lead.
- Check: the order of the decays does not matter; only the totals do. Charge and nucleon number are conserved at every single step, so they are conserved overall.
A nucleus with proton number $92$ emits three α-particles and two β⁻ particles. What is the proton number of the final nucleus?
Each α lowers $Z$ by $2$ and each β⁻ raises it by $1$: $92 - 6 + 2 = 88$.
A neutral atom has $Z$ electrons — the proton number, never $A$. Isotopes differ only in neutrons, so their chemistry is identical. In a decay equation balance both rows: a β$^{-}$ is written $^{0}_{-1}\beta$, so it leaves $A$ unchanged and raises $Z$ by one. And "the nucleus is tiny" means about $10^{-15}\ \text{m}$ — a hundred thousand times smaller than the atom, not ten.
Atomic mass unit 原子质量单位
- The unit $\text{u}$ is set so that $^{12}_{6}\text{C}$ has mass exactly $12\ \text{u}$.
- $1\ \text{u} = 1.66 \times 10^{-27}\ \text{kg}$; a proton and a neutron are each about $1\ \text{u}$, an α-particle about $4\ \text{u}$ with charge $+2e$.
The unified atomic mass unit is defined so that carbon-12 has a mass of exactly 12 u.
Yes — that definition fixes $1\ \text{u} = 1.66 \times 10^{-27}\ \text{kg}$.
You've got it
- α-scattering → atom is mostly empty with a tiny dense nucleus
- $^{A}_{Z}\text{X}$: $Z$ protons, $A$ nucleons, $N = A - Z$ neutrons, $Z$ electrons when neutral; isotopes share $Z$
- nuclear processes conserve nucleon number and charge — balance both rows of every equation