Foundations — Discovery of electron (Thomson, cathode rays), proton (Goldstein), neutron (Chadwick)

Before you can follow the parent note, you need to be fluent in the small alphabet of symbols it fires at you without warning. This page defines every one of them from zero — plain words, then a picture, then why the topic can't live without it.

0. What is "charge" at all?

The whole topic exists because atoms turn out to be made of charged pieces. Without the idea of + and –, "cathode ray bends toward the plus plate" means nothing.

The symbol for the size of a charge is $q$ (or, for the electron specifically, $e$). Its unit is the coulomb, written $\text{C}$.

1. The tube, the cathode, the anode

Look at the figure: two plates inside a sealed glass tube, air pumped out. The red plate on the left is the cathode (–); the black plate on the right is the anode (+). A beam (red arrow) streaks from – to +. Memory hook: the beam is named after where it starts, not where it ends.

Why the topic needs this: every one of the three discoveries happens inside this exact tube. If you don't know which plate is which, "the ray moves opposite to the cathode ray" is a coin-flip.

2. Electric field $E$ — the invisible push

The force a charge $q$ feels in field $E$ is:

Why the topic needs it: this single line is what makes the beam curve toward a plate, and curving is how Thomson weighs the electron.

3. Magnetic field $B$ — the sideways push on movers

The magnetic force on a charge $q$ moving at speed $v$ through field $B$ (with motion and field crossed at right angles) is:

Why two different fields? Thomson's whole method is to make $F_E$ and $F_B$ fight each other and cancel. That cancellation is only possible because one depends on $v$ and the other doesn't — that's how he pins down the speed.

4. Speed $v$, plate length $L$, time $t$, deflection $y$

These four are the "ruler and stopwatch" symbols of the deflection experiment.

Why the topic needs it: $y$ is the thing we actually measure with a ruler on the screen. Everything else in Thomson's formula is set by us; $y$ is nature's answer.

5. Acceleration $a$ and the ratio $e/m$

Put the electric force in: the beam's sideways acceleration is $a=\frac{F_E}{m}=\frac{eE}{m}.$

Here is the punchline symbol of the whole topic:

Why the topic needs it: $e/m$ being the same for every gas and every metal is the fingerprint that proves the electron is one universal particle, present in all matter.

6. The atomic-notation symbols ${}_Z^{A}X$

The neutron section throws a strange stack of numbers at you: ${}_4^9\text{Be}+{}_2^4\text{He}\to {}_6^{12}\text{C}+{}_0^{1}n$

7. Powers of ten and the scary numbers

Numbers like $1.758\times 10^{11}$ and $9.11\times 10^{-31}$ are everywhere. Don't fear them.

Prerequisite map

Equipment checklist

Test yourself — cover the right side and answer aloud.

Connections

• Charge to Mass Ratio — the general $e/m$ technique these symbols build toward.
• Millikan Oil Drop Experiment — supplies $e$ so mass follows from $e/m$.
• Isotopes and Mass Number — where the ${}_Z^{A}X$ notation pays off.
• Thomson Plum Pudding Model — the first model built from the electron.
• Rutherford Nuclear Model — where protons and neutrons end up living.