Chemistry 1.7 - 1.11 - Isotopes and atomic mass

Atomic identity and mass number

At the particle level, the nucleus contains protons and neutrons. Two numbers describe the nucleus without trying to draw it.

The mass number is a count, so it is a whole number. Electrons are not included: "mass number" specifically means the number of protons plus neutrons, not a measured mass in grams.

The atomic number, $Z$, is the number of protons in the nucleus. Every atom of one element has the same proton number, and that number is unique to the element. An atom with 8 protons is oxygen; changing the neutron number does not change that identity, but changing the proton number would make a different element.

Nuclear notation packages these ideas symbolically:

• $\mathrm{X}$ is the element symbol.
• $A$, at the upper left, is the mass number: protons plus neutrons.
• $Z$, at the lower left, is the atomic number: protons.

For example, $^{23}_{11}\mathrm{Na}$ is a sodium atom with mass number 23 and atomic number 11. It must contain 11 protons because the lower number fixes the element; the remaining particles counted by the mass number are neutrons.

Counting subatomic particles

Three relationships turn atomic and mass numbers into particle counts:

The last relationship applies because each proton has relative charge $+1$, each electron has relative charge $-1$, and an atom has no overall charge. It therefore applies to the neutral atoms named in this lesson.

Worked example: aluminium-27

An aluminium atom is written $^{27}_{13}\mathrm{Al}$. Determine its proton, neutron and electron numbers.

1. Read the atomic number: $Z=13$, so the atom contains 13 protons.
2. Use neutrality: an atom has equal proton and electron numbers, so it contains 13 electrons.
3. Subtract to find neutrons: $A-Z=27-13=14$, so it contains 14 neutrons.
4. Sense-check the nucleus: $13+14=27$, which recovers the stated mass number. The 13 positive proton charges and 13 negative electron charges also cancel.

Do not subtract the mass number from the atomic number: the mass number is the larger total. Also do not copy a decimal relative atomic mass from a periodic table and use it as $A$; a particular isotope has its own whole-number mass number.

Isotopes of an element

Because proton number fixes element identity, isotopes keep the same atomic number $Z$. Their different neutron numbers give them different mass numbers $A$. For neutral isotope atoms, the electron number also stays equal to the proton number.