Atomic number and mass number

Two numbers for every atom

How do we tell the atoms of different elements apart? By the number of protons.

An atom is very small, but it has parts. Its centre, the nucleus, holds protons (positive charge) and neutrons (no charge). The electrons (negative charge) move outside the nucleus. Two numbers tell us what is inside any atom: the atomic number and the mass number.

Atomic number

The atomic number, with the symbol $Z$, is the number of protons in the nucleus of an atom. Every atom of an element has the same atomic number, and no two elements have the same one.

• Hydrogen has $Z = 1$, carbon has $Z = 6$, and sodium has $Z = 11$.
• In a neutral atom, the number of electrons is also $Z$.

The atomic number is like the identity card of the element. If an atom has $6$ protons, it is carbon, always. If it has $7$ protons, it is nitrogen. Adding or removing a proton changes the element. This is the order of the periodic table: the elements are arranged by the atomic number, $1, 2, 3, \dots$

Mass number

The protons and neutrons are in the nucleus, and each has a mass of about $1\ \text{u}$. The electrons have almost no mass: an electron is about $\dfrac{1}{1836}$ of the mass of a proton. So the mass of an atom is almost the mass of its nucleus. The mass number, with the symbol $A$, is the total number of protons and neutrons.

So the number of neutrons is

The mass number is always a whole number, because it counts particles. It is not the same as the atomic mass in the periodic table, which is an average and often has a decimal. You will see why in the lesson on isotopes.

Writing the symbol

We write the mass number at the top left of the symbol of the element, and the atomic number at the bottom left.

For example, chlorine with $A = 35$ and $Z = 17$ is written ${}^{35}_{17}\text{Cl}$.

Examples

You should find that changing the neutrons changes the mass number but not the element, and that the charge changes only the electrons.

How to solve a problem

Follow the same steps every time.

1. Protons $= Z$.
2. Electrons $= Z$ for a neutral atom. For an ion, change the electrons by the charge.
3. Neutrons $= A - Z$.

Worked example. An atom of aluminium is ${}^{27}_{13}\text{Al}$. Protons $= 13$. Electrons $= 13$. Neutrons $= 27 - 13 = 14$.

Another way round. An atom has $7$ protons and $7$ neutrons. Then $Z = 7$, so the element is nitrogen. The mass number is $A = 7 + 7 = 14$. The symbol is ${}^{14}_{7}\text{N}$.

Ions

An ion has a different number of electrons, but the same number of protons and neutrons, because the nucleus does not change in a chemical reaction. The ion $\text{Na}^+$ has lost one electron, so it has $10$ electrons. The ion $\text{Cl}^-$ has gained one, so it has $18$.

More examples:

• $\text{Li}^{+}$ ($Z = 3$): lost $1$ electron, so $3 - 1 = 2$ electrons.
• $\text{Al}^{3+}$ ($Z = 13$): $13 - 3 = 10$ electrons.
• $\text{S}^{2-}$ ($Z = 16$): gained $2$ electrons, so $16 + 2 = 18$ electrons.

Notice that $\text{Na}^+$ and $\text{Al}^{3+}$ both have $10$ electrons, the same as the noble gas neon. This is no accident, and the next lessons explain why.

Practise with new numbers

Try it in Python

This program finds the three kinds of particle from $Z$ and $A$.

Common mistakes

• Using the mass number as the number of protons. The number of protons is $Z$.
• Forgetting to subtract. Neutrons are $A - Z$, not $A$.
• Changing the number of protons for an ion. An ion has the same protons as its atom. Only the electrons change.
• Mixing up the positions in the symbol. The mass number is at the top, and the atomic number is at the bottom.
• Thinking that the electrons add to the mass number. They do not. They are almost without mass.

Remember these

• Atomic number $Z$ = number of protons. It identifies the element.
• Mass number $A$ = protons + neutrons.
• Neutrons $= A - Z$. In a neutral atom, electrons $= Z$.
• For an ion, the electrons change by the charge.

Check yourself

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

1. How many protons, neutrons and electrons are there in ${}^{23}_{11}\text{Na}$?

2. An atom has $9$ protons and $10$ neutrons. What are $Z$ and $A$?

3. How many electrons are there in the ion $\text{Li}^{+}$ ($Z = 3$)?

4. Two atoms both have $A = 14$. One has $6$ protons and the other has $7$. Are they the same element?