Quantum physics (HL)

A **quantum (packet) of light energy**, E = hf.

$E = hf$ (or $E = hc/\lambda$); h = 6.63×10⁻³⁴ J s.

Light ejecting **electrons** from a metal surface.

$E_{\max} = hf - \Phi$ (max electron KE = photon energy − work function).

The **minimum energy** needed to free an electron from the metal.

The lowest frequency that ejects electrons: $f_0 = \Phi/h$ (where E_max = 0).

**More** electrons ejected per second; their max KE is **unchanged**.

Max KE **increases** (E_max = hf − Φ).

One electron absorbs **one photon**; a sharp threshold can't be explained by a smooth wave.

**Diffraction** and **interference**.

The **photoelectric effect**.

Light (and matter) behaves as **both** a wave and a particle depending on the experiment.

It gives some of its **energy and momentum** to the recoiling electron; less energy means a longer wavelength.

A **threshold frequency**, E_max set by **frequency** not brightness, and **instant** emission even in dim light.

Gradient **h**; it cuts the f axis at the threshold **f₀** and, extended, the E_max axis at **−Φ**.

The **wave** behaviour of a moving particle, with wavelength λ = h/p.

$\lambda = h/p$ (p = mv for a slow particle).

**Inversely** — bigger momentum gives a **shorter** wavelength.

**Electron diffraction** — electrons make diffraction patterns off crystals.

Its momentum is huge, so λ = h/p is far too small (~10⁻³⁴ m) to notice.

Find **p = mv** first, then **λ = h/p**.

**sin θ ≈ λ/b**: a shorter de Broglie wavelength gives a smaller angle.

They **shrink**: faster electrons have a shorter wavelength, λ = h/√(2meV).

Their λ (~10⁻¹⁰ m) matches the **atomic spacing**.

λ is **halved** (p doubles, λ = h/p).

**metres (m)**.

Particles like electrons show **both** particle and wave behaviour.

**λ = h/√(2meV)**, from λ = h/p and eV = p²/2m.