Extended reading: Moseley and the atomic number

A question that mass could not answer

In the main course, we saw that Mendeleev put the elements in order of atomic mass. A few pairs, such as argon and potassium, were in the wrong order by mass. He moved them by hand, because their properties told him to. But why did the properties follow some other number? Nobody knew.

Moseley's experiment

In $1913$, the young English physicist Henry Moseley sent a beam of fast electrons at about forty different elements, one after the other. Each element gave out X-rays. Each gave a few sharp lines, a kind of fingerprint.

He looked at the strongest line, called the K-alpha line, and he measured its energy.

The straight line

Moseley noticed something simple. If you take the square root of the energy and you put the elements in their order in the table, the points fall on a straight line.

Here $E$ is the energy of the X-ray, $k$ is a constant, and $Z$ is the place of the element in the table, counting from hydrogen as $1$.

The meaning is clear. Each step to the next element adds the same amount to $\sqrt{E}$. So each element differs from the one before it by one unit of something. That something is the positive charge of the nucleus, the number of protons. Moseley named the place number the atomic number.

You should find that every grey dot sits on the line, and that the line meets zero at $Z = 1$.

What the line settled

• Argon and potassium. By mass, potassium comes first. By atomic number, argon ($18$) comes first. The X-rays agree with the properties.
• Tellurium and iodine. The same, for a second pair.
• Gaps. A real element must fall on the line. When Moseley looked at the whole list, there were four places where no known element was on the line: $Z = 43$, $61$, $72$ and $75$. He said that elements must exist there, and that they were not yet found. They were found later: hafnium ($72$) in $1923$, rhenium ($75$) in $1925$, technetium ($43$) in $1937$ and promethium ($61$) in $1945$.
• Not too many. The line also showed that between hydrogen and uranium there are exactly $92$ places. No one could add a hidden element between two others.

Moseley died in $1915$, at the age of $27$, in the First World War. His work stayed. The modern periodic law, the order by atomic number, is his.

Practise with new numbers

Try it in Python

This program fits a straight line through the K-alpha energies of the elements from calcium to zinc, and it finds the atomic number of an unknown element.

Remember these

• Moseley found that $\sqrt{E}$ of the K-alpha X-ray rises in equal steps with the atomic number.
• The atomic number is the number of protons. It is the true order of the elements.
• His line settled argon and potassium, and showed four empty places: $43$, $61$, $72$ and $75$.

Check yourself

Try each one on your own first. If you are stuck, open a hint. Then check with Show the answer.

1. Why does Moseley's straight line mean that each element has one more proton than the one before?

2. Which pair of elements did the line put in order against their masses?

3. After Moseley, why could no hidden element be squeezed between two known ones?

4. By what factor is $\sqrt{E}$ larger for $Z = 31$ than for $Z = 16$?