IB Physics HLTopic 5 — Quantum PhysicsPaper 1 & 2E = hf (photons)~15 min read
Light as a Particle
For a hundred years everyone was sure light was a wave — and with good reason: it diffracts, it interferes, it bends around corners. Then the photoelectric effect showed up and the wave picture simply couldn’t explain it. Einstein’s fix was bold: treat light as a stream of tiny energy bullets called photons. Each photon is a discrete packet of energy that either has enough to free an electron or it doesn’t — no in-between, no gradual build-up. This page is about why that particle picture is forced on us, and exactly where the old wave model breaks down.
📘 What you need to know
Light delivers energy in discrete packets called photons (also called quanta)
Each photon carries energy E = hf — energy is quantised, not continuous
In the photoelectric effect, one electron absorbs exactly one photon — a one-to-one interaction
This explains the threshold frequency: below it, no single photon has enough energy, so no electrons escape
It explains why emission is instant — no waiting for energy to build up
The wave model predicts the opposite: any frequency should work given enough time or intensity, and brighter light should give faster electrons
These wave predictions are not what experiments show — so light must be behaving as particles here
Brighter light of the same colour means more photons, not more energetic ones
Waves vs packets
The heart of the disagreement is how energy arrives. The wave model says energy flows in smoothly and continuously, like water filling a bath — give it long enough and any electron will eventually collect enough to escape. The photon model says energy arrives in discrete lumps, and an electron can only take one lump at a time.
The wave model spreads energy out smoothly (top). The photon model delivers it as separate, equal packets of size hf (bottom) — and only the second picture explains the photoelectric effect.
Energy of a photon (quantised)E = hfh = Planck’s constant • f = frequency • energy comes only in whole-photon lumps
“Quantised” just means energy comes in fixed lumps, never a smooth stream — like buying eggs by the box, not by the gram. An electron can grab one photon-lump but can’t collect half a lump here and half there and add them up. That “all or nothing per photon” rule is the entire reason the wave picture fails, and it’s the seed of the word quantum physics.
Why the wave model fails
Line up what each model predicts against what the experiment actually shows. Every disagreement points the same way — light is behaving as particles.
Observation
Wave model predicts…
Photon model explains it
Below f0, no electrons ever escape
Any frequency should work if bright enough or given time
One photon = hf; too small below f0, so it can’t free an electron
Emission is instant
Energy builds up gradually — there’d be a delay
One photon delivers all its energy at once
Brighter light → more electrons, same speed
Brighter light → faster electrons
Brightness = more photons, but each is still size hf
Higher frequency → faster electrons
Frequency shouldn’t affect electron speed
Bigger photon energy leaves more over as kinetic energy
One photon E = hf
absorbed by
One electron
explains
Threshold & instant emission
WE 1
Green light has a wavelength of 550 nm. Calculate the energy of a single photon of this light, in both joules and electronvolts. (h = 6.63 × 10−34 J s, c = 3.00 × 108 m s−1, 1 eV = 1.60 × 10−19 J)
Step 1 — photon energy from wavelengthE = hc/λ = (6.63 × 10⁻³⁴)(3.00 × 10⁴) / (550 × 10⁻⁹)E = 3.6 × 10⁻¹⁹ JStep 2 — convert to eV (divide by 1.60 × 10⁻¹⁹)E = (3.62 × 10⁻¹⁹) / (1.60 × 10⁻¹⁹)E = 2.3 eVA single visible-light photon carries only a couple of eV — a tiny amount of energy. That’s why everyday light feels smooth: countless photons arrive every second, so you never notice the individual lumps.
How many photons?
Because each photon is such a tiny packet, an ordinary light source pours out an astronomical number every second. Working out “how many photons per second” is a classic exam question: find the energy of one photon, then divide the total power by it.
Photons emitted per secondn = P / E = Pλ / hcP = power of source (W) • E = energy of one photon (J)
WE 2
A red laser pointer emits light of wavelength 650 nm with a power output of 5.0 mW. Calculate the number of photons it emits per second. (h = 6.63 × 10−34 J s, c = 3.00 × 108 m s−1)
Step 1 — energy of one photonE = hc/λ = (6.63 × 10⁻³⁴)(3.00 × 10⁴) / (650 × 10⁻⁹)E = 3.06 × 10⁻¹⁹ JStep 2 — photons per second = power / energy per photonn = P/E = (5.0 × 10⁻³) / (3.06 × 10⁻¹⁹)n = 1.6 × 10¹⁶ photons per secondThat’s about 16 thousand trillion photons every second from a tiny laser pointer! Watch the units: 5.0 mW = 5.0 × 10⁻³ W. Power is energy per second, so dividing by the energy of one photon gives photons per second.
Photon momentum
Here’s the clincher for light-as-a-particle: photons carry momentum, just like any particle. They have no mass, yet a photon striking a surface gives it a tiny push. For a massless particle, momentum links to energy by p = E/c, which tidies up to a lovely form using the wavelength.
Momentum of a photonp = E / c = h / λp = momentum (kg m s−1) • a photon has momentum despite having no mass
A particle with no mass but real momentum sounds impossible — but it’s true, and it’s the seed of the next chapters. That photon momentum is exactly what gets transferred in Compton scattering, and the mirror-image idea (a particle having a wavelength λ = h/p) is the de Broglie relation. Notice the same h/λ appearing — these ideas are all woven together.
WE 3
An X-ray photon has a wavelength of 0.10 nm. (a) Calculate its momentum. (b) Calculate its energy in keV. (h = 6.63 × 10−34 J s, c = 3.00 × 108 m s−1, 1 eV = 1.60 × 10−19 J)
(a) Step 1 — momentum from p = h/λp = (6.63 × 10⁻³⁴) / (0.10 × 10⁻⁹)p = 6.6 × 10⁻²⁴ kg m s⁻¹(b) Step 2 — energy, then convert to keVE = pc = (6.63 × 10⁻²⁴)(3.00 × 10⁴) = 1.99 × 10⁻¹⁵ JE = (1.99 × 10⁻¹⁵) / (1.60 × 10⁻¹⁹) = 1.24 × 10⁴ eVE = 12.4 keVOnce you have momentum, energy is just E = pc for a photon. X-ray photons carry thousands of eV — far more than the ~2 eV of visible light — which is why X-rays are so penetrating and can knock inner electrons out of atoms.
⚛ Working a photon question
Photon energy?E = hf (frequency given) or E = hc/λ (wavelength given).
Energy in eV? Divide the joule answer by 1.60 × 10−19.
Photons per second?n = P/E — total power divided by energy per photon.
Momentum?p = E/c = h/λ.
Explain-why questions? Anchor every point on “one photon, one electron” and “energy comes in lumps of hf.”
💡 Top tips
The photon model’s core claim: energy is quantised in packets of hf, and one electron absorbs one photon.
For “explain the photoelectric effect” answers, always contrast wave prediction with observation.
Brighter light = more photons per second, not more energetic ones.
Photons per second: n = P/E — convert mW to W first.
A photon has momentum p = h/λ even though it’s massless.
⚠ Common mistakes
Saying the wave model explains the threshold frequency — it can’t; that’s the whole point
Thinking one electron can absorb several photons and add them up — it’s strictly one
Claiming brighter light gives faster electrons — it gives more, same speed
Forgetting mW → W in photons-per-second problems
Assuming a massless photon has no momentum — it has p = h/λ
Mixing up frequency (sets photon energy) with intensity (sets photon number)
Quick recap: Light delivers energy as discrete packets called photons, each carrying E = hf — energy is quantised. In the photoelectric effect one electron absorbs one photon, which neatly explains the threshold frequency and the instant emission that the wave model gets wrong. Brighter light means more photons, not stronger ones, so it changes electron number not speed. Photons even carry momentum, p = h/λ, despite being massless — the ultimate proof that light behaves as a particle.
So light — long thought to be a pure wave — also acts like a stream of particles. That raises an irresistible question: if waves can behave like particles, can particles like electrons behave like waves? That’s the astonishing symmetry Louis de Broglie proposed next, giving every moving particle its own wavelength λ = h/p. Next page: The de Broglie Wavelength.
Photons and the particle model still fuzzy?
Book a free meeting and we’ll nail why the wave model fails, the “one photon, one electron” rule, and photon energy & momentum calculations.
