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Pass electricity through a gas at normal pressure and you get a spark. Pump most of the gas out and something stranger happens: the tube glows, and rays stream from the negative electrode. In the 1870s William Crookes built the tubes that made these rays easy to study. This post covers what he saw, why the low pressure mattered, a worked example on the mean free path of gas molecules, and what students can learn from his mix of sharp experiments and a wrong theory.
Who was William Crookes?
Crookes was born in London on 17 June 1832 and died there on 4 April 1919, according to Encyclopaedia Britannica. He studied at the Royal College of Chemistry and, after inheriting a fortune, worked from 1856 in his own private laboratory in London. He discovered the element thallium, discovered the principle of the radiometer, a device that turns light into rotation, and was knighted in 1897.
What did Crookes see in his tubes?
Britannica summarises his findings: a dark space around the negative electrode, now called the Crookes dark space, and rays that travel in straight lines and produce phosphorescence and heat when they strike certain materials.
He described them to a large audience in a lecture to the British Association at Sheffield on 22 August 1879, printed as On Radiant Matter. A full text of the lecture shows how he reasoned. He linked the dark space to "the mean free path of the molecules", the average distance a molecule travels before hitting another. As he pumped more gas out, the dark space grew, just as the mean free path should. He found the effects strongest at about a millionth of an atmosphere.
In one experiment, rays from the electrode hit a metal cross inside a bulb, and a sharp black shadow of the cross appeared on the glowing glass. In his words, radiant matter "comes from the pole in straight lines". The behaviour seemed so different from ordinary gas that he proposed "matter in a fourth state or condition, a condition as far removed from the state of gas as a gas is from a liquid".
Was Crookes right about radiant matter?
Not fully. Britannica says his theory of radiant matter "proved incorrect in many respects". NCERT's Class 12 chapter on atoms records that in 1897 J. J. Thomson's experiments on discharge through gases revealed that atoms contain negatively charged constituents, the electrons. NCERT's Class 11 chemistry chapter on the structure of the atom starts from the same discharge tubes and lists what the rays do: they travel from cathode to anode, make zinc sulphide glow, are bent by electric and magnetic fields as negative particles would be, and behave the same whatever gas or electrode you use. You can follow that next step in our post on J. J. Thomson and the electron.
Worked example: why did the tube need such a good vacuum?
NCERT's Class 11 physics chapter on kinetic theory estimates the mean free path of air molecules at normal pressure as about 2.9 x 10^-7 m, using n = 2.7 x 10^25 molecules per cubic metre and a molecular diameter of d = 2 x 10^-10 m.
The rule: the mean free path is l ∝ 1/n, and at a fixed temperature n ∝ p. So l is inversely proportional to pressure.
Crookes's pressure: about a millionth of an atmosphere, so n falls by a factor of 10^6 and l rises by 10^6.
New mean free path: 2.9 x 10^-7 m x 10^6 = 0.29 m, about 29 cm.
That is the size of a laboratory tube. At this pressure a particle can cross the whole tube without hitting a gas molecule, so it moves in a straight line and casts a sharp shadow. NCERT makes the same point: in a highly evacuated tube the mean free path "can be as large as the length of the tube".
Common mistakes to avoid:
Thinking l depends on pressure directly. Halve the pressure and the mean free path doubles.
Changing the temperature by accident. The simple scaling only holds at constant temperature.
Worrying about the √2. The full formula l = 1/(√2 nπd²) gives about 2.1 x 10^-7 m at normal pressure instead of 2.9 x 10^-7 m. Either way it is a fraction of a micrometre, and the factor of a million is what matters.
Our guide to the mean free path of gas molecules has more practice.
What can a student take from how Crookes worked?
Control the conditions. Better pumps let him change one thing, pressure, and watch the effect.
Design experiments that answer yes or no. A metal cross either casts a sharp shadow or it does not.
Hold theories loosely. His observations led to the electron even though his own explanation was wrong.
Show, do not just tell. In the Sheffield lecture he set out to make the dark space "visible to all present".
For the positive rays that appear in the same tubes, read our post on Eugen Goldstein and canal rays. If terms like mean free path or discharge tube still feel shaky, the Fermi Concept Library covers every concept in physics and chemistry and shows what each one builds on.
Next step: work out the mean free path at a thousandth of an atmosphere and check that you get about 0.29 mm.
