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A Geiger counter clicks once for each particle it detects. That simple idea, turning one invisible particle into one countable signal, made much of early nuclear physics possible. Hans Geiger spent most of his career building better ways to count. This post covers his life, the experiments he made possible, and two counting problems you can solve with the same reasoning.
Who was Hans Geiger?
The Neue Deutsche Biographie records that Johannes (Hans) Wilhelm Geiger was born on 30 September 1882 in Neustadt an der Weinstraße and died on 24 September 1945 in Potsdam. He studied in Munich and Erlangen, taking his doctorate at Erlangen in 1906. From 1906 to 1912 he worked at the University of Manchester as a collaborator of Ernest Rutherford on radioactivity.
In 1912 he took over the radioactivity laboratory of the Physikalisch-Technische Reichsanstalt in Berlin. He became a professor at Kiel in 1925, moved to Tübingen in 1929 and to the Technische Hochschule in Berlin-Charlottenburg in 1936. Serious illness from 1943 and being forced from his home at the end of the war contributed to his death.
How do you count a single alpha particle?
In 1908, Rutherford and Geiger published An electrical method of counting the number of α-particles. Their abstract explains the problem. Earlier estimates of how many alpha particles a gram of radium emits per second depended on assuming the charge each one carried. A direct count would remove that assumption, so measuring the total charge would then give the charge per particle. That would help settle the most pressing question in radioactivity at the time: whether an alpha particle is a helium atom.
The NDB describes their instrument as a development of the ionisation chamber that, for the first time, detected individual alpha particles. It also credits Geiger, in 1908, with confirming the statistical character of radioactive decay. In 1910 Rutherford, Geiger and the mathematician Harry Bateman published a paper on the probability variations in the distribution of α particles, looking at how the number arriving in equal time intervals varies by chance.
Which famous experiment did Geiger help start?
In 1909 Geiger and Ernest Marsden reported a diffuse reflection of the α-particles. They found that a small fraction of alpha particles falling on a metal plate had their directions changed so much that they came back out on the side they entered. The NDB notes that these scattering experiments led to Rutherford's scattering formula and his model of the atom. Our post on Rutherford's gold foil experiment tells that part of the story.
In 1911 Geiger and John Nuttall found the link between the range of alpha rays and the half-life of the substance emitting them. In 1925, with Walther Bothe, he used a point counter to show that the scattered quantum and the recoil electron in the Compton effect appear at the same time.
What was new about the Geiger-Müller tube?
At Kiel, Geiger and his student Walther Müller published the first paper on the Geiger-Müller counter tube in Physikalische Zeitschrift in 1928 (volume 29, pages 839–41), according to the NDB. The NDB notes that the counter tube found use throughout technology and came to be manufactured industrially in many forms.
Worked example 1: half-life from a counter
A counter near a sample records 820 counts per minute. With the sample removed, it records 20 counts per minute from background radiation. Ten minutes later, with the sample back, it reads 220 counts per minute.
Remove the background: 820 − 20 = 800 per minute at the start; 220 − 20 = 200 per minute after ten minutes.
Compare: 800 → 200 is a fall to one quarter, which is two halvings (800 → 400 → 200).
Half-life: two half-lives in 10 minutes, so the half-life is 5 minutes.
If you forget the background, you compare 820 with 220, a ratio of about 3.7, and get the wrong half-life.
Worked example 2: how sure is a count?
Because decay is random, a count N has a typical spread of about √N. Suppose you record 400 counts in 100 s.
Rate: 400 / 100 = 4.0 counts per second.
Spread: √400 = 20 counts, so the rate is 4.0 ± 0.2 counts per second.
Relative spread: 20 / 400 = 5%. To halve it to 2.5% you need four times the counts, 1600, which means counting for 400 s.
Mistakes to avoid:
Skipping background. Subtract it from every reading before comparing.
Halving the time instead of the count. Half-life is the time for the rate to halve.
Trusting small counts. Ten counts have a spread of about three, so a single short reading tells you little.
Our guide to radioactive decay and half-life has more problems of this type. If you want to see why random decay still gives a smooth curve, the Fermi Simulation Lab has interactive simulations for ideas that are easier to see than read.
What can a student take from how he worked?
Improve the measurement, not just the theory. A better counter answered questions that argument alone could not.
Remove assumptions. Counting particles directly replaced a guess about their charge.
Respect randomness. He treated chance variation as something to measure, not ignore.
Work in teams. Rutherford, Marsden, Nuttall, Bothe and Müller each shared in his most famous results.
Try it: a background-corrected rate falls from 640 to 80 counts per minute in 24 minutes. What is the half-life?
