Atomic Number and Mass Number Notation for HSC Chemistry

Two atoms can both be carbon even when one has 6 neutrons and the other has 8. That sounds odd at first. If the nuclei are different, why are they still the same element?

Before reading on, predict which number must stay the same for both atoms to remain carbon: the number of protons, the number of neutrons, or the total number of particles in the nucleus.

It has to be the number of protons. The proton number determines the element. Neutrons can change without changing the element, which is why we need isotope notation.

01The two numbers you need to track

Picture the nucleus as a small bag containing only protons and neutrons.

There are two useful counts:

• Atomic number, \(Z\): the number of protons.
• Mass number, \(A\): the total number of protons and neutrons.

If \(N\) is the number of neutrons, then:

\[
A = Z + N
\]

and therefore:

\[
N = A – Z
\]

The symbols mean:

• \(A\) = mass number, with no unit
• \(Z\) = atomic number, with no unit
• \(N\) = number of neutrons, with no unit

These are counts of particles, so they don’t have units.

For example, a nucleus containing 6 protons and 8 neutrons has:

\[
A = 6 + 8 = 14
\]

Because \(Z = 6\), the element is carbon. This particular atom is carbon-14.

02How isotope notation works

An isotope symbol is written in this form:

\[
\ce{^{A}_{Z}X}
\]

Here:

• \(X\) is the chemical symbol
• \(A\) is the mass number
• \(Z\) is the atomic number

For carbon-14:

\[
\ce{^{14}_{6}C}
\]

Read it from the bottom first if that helps:

1. \(Z = 6\), so there are 6 protons. Atomic number 6 identifies carbon.
2. \(A = 14\), so there are 14 nucleons altogether.
3. The neutron count is \(14 – 6 = 8\).

A nucleon simply means a proton or neutron. That is why mass number is also called nucleon number.

A useful mental model

Think of the atomic number as an element’s identity card. If the proton number changes, you’ve changed the element.

The mass number is more like the number of people in a group photo. You can add or remove neutrons and still have the same “person”, meaning the same element, but the total headcount changes.

The analogy stops working if you push it too far. Protons and neutrons are not interchangeable people. Changing the proton number changes the nuclear charge and therefore the element itself.

03Isotopes have the same atomic number

Suppose you have:

\[
\ce{^{12}_{6}C}
\qquad \text{and} \qquad
\ce{^{14}_{6}C}
\]

What is the same?

Both have \(Z = 6\), so both contain 6 protons. They are both carbon.

What is different?

Their mass numbers are 12 and 14.

For carbon-12:

\[
N = 12 – 6 = 6
\]

For carbon-14:

\[
N = 14 – 6 = 8
\]

So isotopes are atoms of the same element with the same number of protons but different numbers of neutrons.

That produces the key pattern:

04How to construct an isotope symbol

Sometimes the question goes the other way. Instead of reading a symbol, you are given information about the nucleus and must build the notation.

Use this order:

1. Find the number of protons. This gives \(Z\).
2. Use \(Z\) to identify the element.
3. Add protons and neutrons to find \(A\).
4. Put \(A\) at the upper left and \(Z\) at the lower left.

05The most common trap: mass number is not the periodic-table atomic mass

Look at chlorine on a periodic table and you may see a value close to 35.45.

Should you write \(A = 35.45\) in an isotope symbol?

No.

A mass number counts protons and neutrons in one particular nucleus, so it must be a whole number. You cannot have 0.45 of a neutron sitting around in the nucleus.

The decimal value on a periodic table is usually the relative atomic mass. It is influenced by the masses and relative abundances of the naturally occurring isotopes of that element.

So these are different ideas:

The fact that relative atomic mass is often not a whole number is not a problem. It is an average, not the particle count in a single nucleus.

You can build that idea further in Relative Atomic Mass from Isotopic Composition.

06A fast decision rule

When you see nuclear notation, ask these questions in order:

1. What is \(Z\)? That gives the number of protons and identifies the element.
2. What is \(A\)? That gives the total number of protons and neutrons.
3. Need neutrons? Calculate \(A – Z\).
4. Comparing isotopes? Check that \(Z\) is the same and \(A\) is different.
5. See a charge at the upper right? Keep it separate. Charge changes the electron count, not the isotope’s proton or neutron numbers.

07Questions and solutions

Question 1

For the isotope \(\ce{^{27}_{13}Al}\), state the atomic number, mass number, number of protons, and number of neutrons.

Solution 1

The isotope has atomic number 13, mass number 27, 13 protons, and 14 neutrons.

The lower-left number is the atomic number:

\[
Z = 13
\]

So there are 13 protons.

The upper-left number is the mass number:

\[
A = 27
\]

The neutron number is:

\[
N = A – Z = 27 – 13 = 14
\]

Therefore, \(\ce{^{27}_{13}Al}\) contains 13 protons and 14 neutrons. The common mistake is to treat 27 as the neutron count. It is actually the total number of protons and neutrons.

Question 2

An atom contains 20 protons and 22 neutrons. Construct its isotope symbol.

Solution 2

The isotope symbol is \(\ce{^{42}_{20}Ca}\).

The atomic number is the number of protons:

\[
Z = 20
\]

Atomic number 20 corresponds to calcium, \(\ce{Ca}\).

The mass number is:

\[
A = Z + N = 20 + 22 = 42
\]

Therefore:

\[
\ce{^{42}_{20}Ca}
\]

This is calcium-42. The important step is identifying the element from \(Z = 20\), not from the mass number 42.

Question 3

Consider \(\ce{^{35}_{17}Cl}\) and \(\ce{^{37}_{17}Cl}\).

Are they isotopes of the same element? State the number of neutrons in each nucleus and explain your conclusion.

Solution 3

Yes. They are isotopes of chlorine, containing 18 and 20 neutrons respectively.

Both nuclei have:

\[
Z = 17
\]

so both contain 17 protons. The same proton number means they are the same element.

For \(\ce{^{35}_{17}Cl}\):

\[
N = 35 – 17 = 18
\]

For \(\ce{^{37}_{17}Cl}\):

\[
N = 37 – 17 = 20
\]

They have the same atomic number but different mass numbers because they contain different numbers of neutrons. That is exactly what makes them isotopes.

Question 4

A student wants to represent argon-40 and writes \(\ce{^{18}_{40}Ar}\).

Explain what is wrong with the notation and write the correct isotope symbol.

Solution 4

The numbers have been reversed. The correct symbol is \(\ce{^{40}_{18}Ar}\).

Argon has atomic number:

\[
Z = 18
\]

The atomic number must therefore appear at the lower left.

The name argon-40 tells us that its mass number is:

\[
A = 40
\]

The mass number belongs at the upper left.

So the correct notation is:

\[
\ce{^{40}_{18}Ar}
\]

The student’s version is not just untidy notation. If \(Z\) really were 40, the nucleus would contain 40 protons and would not be argon at all. The chemical symbol and atomic number must agree.

Question 5

Three species are shown:

\[
\ce{^{40}_{18}Ar}
\qquad
\ce{^{40}_{19}K+}
\qquad
\ce{^{41}_{19}K+}
\]

Identify which two species are isotopes of the same element. Then identify a pair that has the same mass number but is not a pair of isotopes. Explain why the \(+\) charge does not affect either decision.

Solution 5

\(\ce{^{40}_{19}K+}\) and \(\ce{^{41}_{19}K+}\) are isotopes. \(\ce{^{40}_{18}Ar}\) and \(\ce{^{40}_{19}K+}\) have the same mass number but are not isotopes.

The two potassium species both have:

\[
Z = 19
\]

so they have the same number of protons and are the same element. Their mass numbers differ:

\[
A = 40 \quad \text{and} \quad A = 41
\]

Therefore, they are isotopes.

Argon-40 and potassium-40 both have:

\[
A = 40
\]

but their atomic numbers are different:

\[
Z_{\ce{Ar}} = 18
\qquad
Z_{\ce{K}} = 19
\]

So they are different elements. Having the same mass number does not make two nuclei isotopes.

The \(+\) charge tells us that the potassium species has lost an electron. Losing an electron does not alter the nucleus, so it does not change \(A\), \(Z\), or isotope identity.

The tempting mistake here is to focus on the matching number 40. For isotope comparisons, the first thing to compare is always \(Z\).

Question 6

Two neutral atoms each contain 20 neutrons. Atom P has mass number 39, while atom Q has mass number 40.

A student argues that they must be isotopes because they have the same number of neutrons. Determine the identity of each atom and assess the student’s claim.

Solution 6

Atom P is potassium-39, atom Q is calcium-40, and they are not isotopes.

For atom P:

\[
Z = A – N = 39 – 20 = 19
\]

Atomic number 19 is potassium, so atom P is:

\[
\ce{^{39}_{19}K}
\]

For atom Q:

\[
Z = A – N = 40 – 20 = 20
\]

Atomic number 20 is calcium, so atom Q is:

\[
\ce{^{40}_{20}Ca}
\]

The student’s reasoning fails because isotopes are defined by having the same proton number, not the same neutron number.

These atoms happen to contain 20 neutrons each, but one has 19 protons and the other has 20. Their atomic numbers are different, so they are different elements.

That distinction becomes especially useful once nuclear reactions are introduced. In a nuclear equation, keeping track of mass number and atomic number lets you work out what particles or nuclei must have formed and whether the equation is balanced.