Structure of the atom

**Proton** (+1) and **neutron** (0) in the nucleus; **electron** (−1) around it.

A particle found **in the nucleus** — i.e. a **proton or a neutron**.

A specific type of nucleus, fixed by its number of **protons and neutrons** (e.g. carbon-14).

**A** (top) = nucleon number = protons + neutrons. **Z** (bottom) = proton number = number of protons.

**N = A − Z** (nucleon number minus proton number).

**electrons = Z − q.** A 2+ ion has Z − 2 electrons; a 1− ion has Z + 1.

Only the **electron** count. Protons and neutrons (the nucleus) are unchanged.

Most passed **straight through**; a few deflected through **large angles**; a very few **bounced straight back**.

The atom is **mostly empty space**.

The positive charge and almost all the mass are in a **tiny, dense, positively charged nucleus**.

A small, fast, positive particle = **2 protons + 2 neutrons** (a helium nucleus).

An electron's mass is about **1/2000** of a nucleon's — negligible next to protons and neutrons.

An atom can only have certain **fixed** allowed energies — never the values in between (like stairs, not a ramp).

A single tiny **packet of light energy**. Its energy is given by E = hf = hc/λ.

It **emits a photon** whose energy equals the **gap** between the two levels (an emission line).

An electron **jumps up** to a higher level — but only if the photon's energy exactly matches a level **gap**.

$E = hf$ — energy = Planck constant × frequency (given in the data booklet).

$E = \dfrac{hc}{\lambda}$ — bigger energy means shorter wavelength (given).

The one with the **smallest** energy drop — because E = hc/λ, a small energy means a large wavelength.

The **biggest** energy drop — more energy means a shorter wavelength (and higher frequency).

**n(n − 1) ÷ 2** distinct wavelengths. E.g. n = 3 → 3 lines; n = 4 → 6 lines.

Emission = **bright lines** on dark (electron falls, photon out). Absorption = **dark lines** in a rainbow (electron rises, photon in). Same atom → same line positions.

Each element has its **own** set of energy levels, so its own unique pattern of lines — you can match a spectrum to an element.

λ = hc/E = (6.63 × 10⁻³⁴ × 3.00 × 10⁸) / (3.0 × 10⁻¹⁹) ≈ 6.6 × 10⁻⁷ m.

The **energy gained by one electron** when it moves through a potential difference of **one volt**. It is a unit of energy.

**1 eV = 1.60 × 10⁻¹⁹ J** — given in the data booklet.

Energy = charge × voltage. The electron's charge e = 1.60 × 10⁻¹⁹ C, so crossing 1 V gives it 1.60 × 10⁻¹⁹ J.

**Multiply** the number of eV by 1.60 × 10⁻¹⁹.

**Divide** the energy in joules by 1.60 × 10⁻¹⁹.

**1 keV = 10³ eV** (a kilo-electronvolt).

**1 MeV = 10⁶ eV** (a mega-electronvolt). Nuclear energies are usually quoted in MeV.

Atomic and nuclear energies are tiny fractions of a joule; the eV gives convenient, easy-to-read numbers.

A **few eV** (about 2 eV) — that is why atomic transitions emit visible light.

A **few MeV** — about a million times bigger than an atomic-transition energy.

**Joules (J).** Convert to eV at the end (÷ 1.60 × 10⁻¹⁹) only if the question asks for eV.

5.0 × 1.60 × 10⁻¹⁹ = **8.0 × 10⁻¹⁹ J** (eV → J, so multiply).

Charge only comes in **whole-number multiples** of the elementary charge e — never a fraction of e. It changes in fixed steps.

**e = 1.60 × 10⁻¹⁹ C** — the charge on one proton (+e) or one electron (−e). The smallest 'lump' of charge. Given in the data booklet.

$Q = N e$ — total charge = whole number N of elementary charges. Rearranged: $N = \dfrac{Q}{e}$.

Use **N = Q ÷ e**. The answer must be a **whole number**.

Because you can only add or remove **whole** electrons — charge changes in steps of e, so N is always a whole number.

It has **gained extra electrons**. (A positively charged object has **lost** electrons.) Each electron carries −e.

Every measured drop charge was a **whole-number multiple of the same smallest step**, e — the experimental proof that charge is **quantised**.

**No.** N = Q ÷ e = 2.4 × 10⁻¹⁹ ÷ 1.60 × 10⁻¹⁹ = 1.5, not a whole number — so it is not allowed.

N = Q ÷ e = 6.4 × 10⁻¹⁹ ÷ 1.60 × 10⁻¹⁹ = **4** electrons.

**No** — it is the definition of charge quantisation, so memorise it. But the constant **e = 1.60 × 10⁻¹⁹ C** IS given.

Each half gets **4e** (8e ÷ 2). Still a whole multiple of e, so allowed.