Calculating particle numbers

A proton has relative charge $+1$, a neutron has charge $0$, and an electron has relative charge $-1$. An atom is electrically neutral, so its positive and negative charges balance. It therefore has equal numbers of protons and electrons.

Atomic number fixes the element

The atomic number, often written $Z$, is the number of protons in the nucleus:

$Z=\text{number of protons}$

Every atom of the same element has the same atomic number. For example, every carbon atom has 6 protons, while every sodium atom has 11. Changing the number of protons would therefore change the element itself.

For a neutral atom:

$\text{number of electrons}=\text{number of protons}=Z$

Thus a neutral atom with atomic number 15 contains 15 protons and 15 electrons.

Mass number reveals the neutron count

The mass number, often written $A$, is the total number of protons and neutrons in one nucleus:

$A=\text{number of protons}+\text{number of neutrons}$

Rearranging gives the rule used to calculate neutrons:

$\text{number of neutrons}=A-Z$

Suppose a neutral atom has atomic number 15 and mass number 31. It has 15 protons, 15 electrons and $31-15=16$ neutrons. Notice that electrons are not included in the mass number.

Reading isotope notation

An isotope may be written in the form ${}^{A}_{Z}\mathrm{X}$, where $\mathrm{X}$ is the element symbol. The larger upper number is the mass number and the smaller lower number is the atomic number.

For ${}^{14}_{6}\mathrm{C}$:

• $Z=6$, so there are 6 protons;
• the atom is neutral, so there are 6 electrons;
• $A=14$, so there are $14-6=8$ neutrons.

Carbon-12 and carbon-14 are isotopes because both have 6 protons but they have different neutron counts. Their common proton number makes both of them carbon; their different neutron numbers give them different mass numbers.

Extracting information from the Periodic Table

The Periodic Table supplies an element’s name, symbol and atomic number. The atomic number directly gives the number of protons and, for a neutral atom, the number of electrons.

To calculate the exact number of neutrons, you also need the mass number of the particular isotope. A mass number is always a whole number because it counts particles. It may be supplied in isotope notation, in a name such as carbon-14, or directly in the question.

Do not confuse mass number with relative atomic mass. The relative atomic mass printed in a Periodic Table is a weighted mean for the element’s naturally occurring isotopes, so it is often not a whole number. For example, a decimal relative atomic mass describes an average rather than the nucleus of one atom. Use a stated isotope’s mass number when an exact neutron count is required.

A reliable calculation method

Work through questions in this order:

1. Read $Z$, the atomic number.
2. Set the proton count equal to $Z$.
3. For an atom, set the electron count equal to $Z$.
4. Read $A$, the mass number of the isotope.
5. Calculate neutrons using $A-Z$.

For sodium-23, the Periodic Table gives sodium atomic number 11. The atom therefore contains 11 protons and 11 electrons, while its neutron count is $23-11=12$. These three results are consistent: the proton count identifies sodium, equal proton and electron counts make the atom neutral, and the proton and neutron counts add to its mass number.