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CED objectives

Quantum Theory and Wave-Particle Duality

▶︎  Watch it animatedinteractive step-through · ~3 min · optional ⚙︎  Open the appletPhoton Ledger · set the colour and the lamp power separately, watch which readout each one moves, then give a proton a wavelength

A photon's energy is set by frequency alone, $E = hf = hc/\lambda$, while intensity counts how many photons arrive per second, so the two are independent knobs. The formula works in either of two matched unit systems, $h$ in J$\cdot$s with $\lambda$ in metres, or $hc = 1240$ eV$\cdot$nm with $\lambda$ in nanometres, and blending them shifts the exponent enormously. One description of light covers both wave and particle behaviour, with the experiment deciding which appears, and every particle with momentum has a de Broglie wavelength $\lambda = h/p$, which grows longer as the momentum gets smaller.

Four errors dominate. Reading intensity as photon energy, so turning up a lamp is expected to make each photon more energetic and every threshold becomes a brightness threshold. Mixing the two unit systems for $h$, or feeding nanometres into a formula that expects metres. Treating light as switching between wave and particle, which leaves no account of why single photons still build an interference pattern. And restricting $\lambda = h/p$ to electrons, or inverting it so that a faster particle is expected to carry a longer wavelength.

two independent knobs RED 2.0 eV each BLUE 3.1 eV each DIM: few per second BRIGHT: many per second across a row: same size of dot, more of them. Down a column: same count, bigger dots turning up the brightness never turns a red photon into a blue one
The dot size is the energy per photon and the number of dots is the rate. Moving right changes only one of them and moving down changes only the other.
photons sent one at a time, accumulating on a screen a few photons: single dots more: a hint of structure many: an interference pattern each photon lands as ONE dot, and the accumulation is a WAVE pattern nothing switched. Electrons do exactly the same thing
Both behaviours are present in every panel. Which one you notice depends on how many arrivals you have collected, not on what the light decided to be.

The work

3 ways in · any order
Lesson
Quantum Theory and Wave-Particle Duality ›

Separates photon energy from beam intensity, keeps the joule and electronvolt unit systems apart, replaces switching between wave and particle with one description, and applies de Broglie to every particle.

Skill check · 10 scenarios
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Diagnostic
10-item topic check ›

Ten items spanning the failure modes of this topic: reading brightness as photon energy, blending the two sets of units, having light switch between wave and particle, and inverting or restricting the de Broglie relation. Take it cold to find which one is yours, or after the lesson to confirm it is not.

Not started · 10 items · ~15 min
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Targeted Practice
Drill a single misconception ›

Pick one of the failure modes you missed and drill it on its own. The round is adaptive: two correct in a row clears it for now and moves you to the next. Two in a row is a checkpoint, not proof: if the error resurfaces later, the misconception comes back.

Take the diagnostic to identify your misconceptions
Diagnostic first