Foundations — Photoelectric effect — Einstein's photon model

This page builds the toolkit the parent topic leans on. We assume you have never seen $h\nu$, "eV", "work function", or a stopping-potential graph. We earn every symbol before using it.

0. The picture we keep returning to

Look at the figure: a metal plate on the left, a packet of light (the red dot) flying in, and one electron flying out on the right. Every symbol below is a label on some part of this one picture — either the incoming packet, the escape cost, or the electron's leftover speed. Hold this image in your head.

1. Energy — the currency of the whole story

Picture: think of energy as coins. To do anything (kick out an electron) you must have enough coins. This "coin" picture returns again and again — the whole topic is a transaction.

Why the topic needs it: the photoelectric effect is an energy accounting problem. Energy in = energy spent escaping + energy left over. You cannot read that sentence without the idea of energy.

2. Frequency $\nu$ and wavelength $\lambda$ — describing a wave

Light, before Einstein, was thought of as a wave. A wave is a repeating up-and-down pattern.

Picture: in the figure, the top wave is stretched out — long $\lambda$, few ripples per second, low $\nu$ (this is red light). The bottom wave is squeezed — short $\lambda$, many ripples per second, high $\nu$ (this is blue/UV light). Notice the seesaw: squeeze the wavelength and the frequency goes up.

Why this tool and not another? We need a single number that captures "colour". Wavelength or frequency both do it, and because $c=\nu \lambda$ they carry the same information. The topic prefers frequency because — as we'll see — energy turns out to be directly proportional to $\nu$, not to $\lambda$. See Electromagnetic Spectrum for the full range of colours this describes.

3. Planck's constant $h$ — the exchange rate between frequency and energy

Here is the leap. Max Planck (see Planck's Quantum Theory) found that light's energy comes in lumps, and each lump's size is set by its frequency through one universal number.

Picture: imagine a vending machine with a fixed price list. Feed in a frequency, out comes exactly $h\nu$ joules of energy per packet — never a bit more, never a bit less.

Why this tool? Classical physics said energy depends on brightness. Planck's $h$ lets us instead tie energy to colour ($\nu$) — exactly the fix the experiment demanded.

4. The photon — the packet itself

Picture: in figure s01 the red dot IS a photon. A dim beam is a few dots; a bright beam is many dots — but every dot is the same size for a given colour.

Why the topic needs it: this single idea — "many identical packets, one packet per electron" — is the entire resolution of the photoelectric mystery. It is Wave-Particle Duality in action: light behaves as particles here.

5. The electron $e$ and its charge

Picture: the flying-out particle in figure s01 is the electron; its charge $e$ is what lets a voltage push back on it later (Section 8).

6. The electron-volt (eV) — a coin the right size

Joules are absurdly big for one electron. We need smaller change.

Why this tool? Working examples in eV and nm keeps every number between roughly 1 and 10 instead of $10^{-19}$. Same physics, kinder arithmetic.

7. Work function $\varphi$ and threshold frequency ${\nu }_0$ — the escape toll

An electron is held inside the metal. Freeing it costs energy.

Picture: the figure shows a well/pit. The electron sits at the bottom; the wall height is $\varphi$. A small photon (too few coins) cannot lift it over the wall — it slides back, no emission. A big photon lifts it over with energy to spare, and that spare energy becomes speed.

Why the topic needs it: $\varphi$ is the "cost to escape" term in the energy budget. Without it there'd be no threshold — and the threshold is the whole point.

8. Kinetic energy $K{E}_{\max }$, speed $v_{\max }$, and stopping potential $V_0$

Putting the whole budget together (this is the parent's central equation, now with every symbol earned):

How do we measure that leftover? We push back on the escaping electrons with a voltage until even the fastest one is stopped.

Picture: imagine the electron rolling uphill against the voltage; make the hill just tall enough and it stops right at the top. That hill height is $V_0$.

9. Slope, and reading a graph

Rearranging $e{V}_0=h\nu -\varphi$: $V_0=\frac{h}{e}\nu -\frac{\varphi }{e}$

Picture: plot $V_0$ (up) against $\nu$ (across) and you get a straight line. Its slope is $h/e$ — measure the steepness and you've measured Planck's constant. Its horizontal intercept is ${\nu }_0$.

Why the topic needs it: this turns an abstract constant into something you read off a ruler-straight graph — the experimental triumph of the model.

Prerequisite map

Read it top-down: waves give frequency, frequency plus $h$ gives the photon's energy, the photon meets the work function in the Einstein equation, and the leftover energy is measured as a stopping potential on a straight-line graph.

Equipment checklist

Test yourself — cover the right side.