From Atomic Mass to Atomic Number

Introduction

Mendeleev's table worked brilliantly, but it had a puzzle at its heart. In a few places he had to put a heavier element before a lighter one to keep similar elements together. Was atomic mass really the right ordering principle? In 1913 a young English physicist, Henry Moseley, found the answer. His experiments showed that each element has a whole-number atomic number , equal to the number of protons in its nucleus, and that this — not mass — fixes its place in the table.

Core explanation

The problem with mass. Ordering by atomic mass left several awkward pairs:

Pair Relative atomic masses Order by properties --- --- --- Argon and potassium Ar 39.9, K 39.1 Ar before K Cobalt and nickel Co 58.9, Ni 58.7 Co before Ni Tellurium and iodine Te 127.6, I 126.9 Te before I

Argon is an unreactive noble gas and potassium is a reactive metal; placing them by mass would put each in completely the wrong group.

Moseley's experiment. Moseley fired high-energy electrons at targets made of different elements. Each target gave off X-rays of characteristic frequencies. He found that when elements were listed in order, the square root of the X-ray frequency increased in equal steps from one element to the next. Each step corresponded to adding one unit of positive charge to the nucleus. He called the position in this sequence the atomic number.

Atomic number is the number of protons. We now know that the nuclear charge Moseley measured comes from protons. Hydrogen has 1 proton, helium 2, lithium 3, and so on. Every atom of a given element has the same number of protons, so atomic number is the element's identity card.

The modern periodic law. When the elements are arranged by atomic number, all the awkward pairs fall into the right order automatically: argon (18) comes before potassium (19), cobalt (27) before nickel (28), tellurium (52) before iodine (53). Mendeleev's instinct was right — he simply lacked the correct ordering property. The modern periodic law states that the properties of elements repeat periodically with atomic number.

Why masses can be out of order. Atomic mass depends on protons and neutrons, and most elements are mixtures of isotopes. Argon is mostly argon-40, while potassium is mostly potassium-39, so argon has the higher average mass despite having one fewer proton.

Finding gaps. Moseley's method also showed exactly which atomic numbers were missing. Between aluminium (13) and uranium (92) he identified gaps at 43, 61, 72 and 75. Elements 72 (hafnium) and 75 (rhenium) were found in the 1920s; 43 (technetium) and 61 (promethium) have no stable isotopes and were made or identified later.

A short life. Moseley was killed in the First World War at Gallipoli in 1915, aged 27. Many scientists believe he would otherwise have received a Nobel Prize.

Step-by-step reasoning

To decide the order of two elements:

1. Look up the atomic number (proton number) of each. 2. Place the element with the smaller atomic number first. 3. Ignore atomic mass for ordering; it may be out of step because of isotopes. 4. Check that each element now lines up with a group of similar elements.

Visual explanation

Picture a staircase of X-ray measurements. Plotting the square root of X-ray frequency against atomic number gives a straight line: each element is exactly one equal step higher than the one before. A missing step on the staircase instantly reveals an undiscovered element.

Real-world analogy

Seats in a theatre are ordered by seat number, not by the weight of the person sitting in them. A heavier person might sit in seat 18 and a lighter one in seat 19. Atomic number is the seat number; atomic mass is just how heavy the occupant happens to be.

Real-world example

X-ray fluorescence analysers, based on the same physics as Moseley's experiment, are used today to identify the elements in metal alloys, soils, paints and even valuable artworks. Each element gives off characteristic X-rays that reveal its atomic number without damaging the sample.

Why?

Why is proton number more fundamental than mass? Because chemical properties depend on electrons, and a neutral atom has as many electrons as protons. Changing the number of neutrons changes the mass but not the electrons, so it hardly changes the chemistry. Atomic number therefore controls behaviour.

Common misconception

"Elements are arranged in the periodic table in order of increasing mass." They are arranged in order of increasing atomic number. Mass usually increases too, but not always, as argon and potassium show.

Worked example

Question: Cobalt has 27 protons and a relative atomic mass of 58.9. Nickel has 28 protons and a relative atomic mass of 58.7. Which comes first in the modern table, and why might Mendeleev have hesitated?

Reasoning: The modern table orders by atomic number: 27 comes before 28. By mass alone, nickel (58.7) would come first.

Answer: Cobalt comes first. Mendeleev had only masses, which suggested the opposite order, so he had to rely on properties.

Quick check

1. What does the atomic number of an element tell you about its atoms? Answer: The number of protons in the nucleus of each atom.

Exam focus

Explain the argon–potassium or tellurium–iodine pair clearly: ordering by atomic number puts them in the correct groups, and the mass reversal is caused by the isotopes present. Remember that the modern periodic table is ordered by atomic (proton) number.

Advanced insight

Moseley's law can be written as √f = a(Z − b), where f is the X-ray frequency, Z is the atomic number and a and b are constants. The constant b accounts for inner electrons partly shielding the nuclear charge — an early hint of the idea of shielding, which later explains many periodic trends.

Summary

Mendeleev ordered elements by atomic mass, which forced him to reverse a few pairs. Henry Moseley's X-ray experiments in 1913 showed that each element has an atomic number equal to its number of protons. Ordering by atomic number places every element correctly, removes the reversals and reveals missing elements. Isotopes explain why atomic mass is sometimes out of step.

Practice questions

1. What property is the modern periodic table ordered by? Answer: Atomic number (proton number). 2. Argon (atomic number 18) has a greater relative atomic mass than potassium (atomic number 19). Explain how this is possible. Answer: Most argon atoms are argon-40 with 22 neutrons, while most potassium atoms are potassium-39 with 20 neutrons, so argon's average mass is higher even though it has fewer protons. 3. Why does ordering by atomic number put elements in groups with similar properties? Answer: Atomic number equals the number of electrons in a neutral atom, and electron arrangement controls chemical properties. 4. How did Moseley's work help find undiscovered elements? Answer: His X-ray measurements increased in equal steps, so a missing step showed exactly which atomic number had no known element.