Calculating Protons, Neutrons, and Electrons in Neutral Atoms

Hello again. Last lesson established the two numbers in nuclear notation: the atomic number is the number of protons, and the mass number is the combined number of protons and neutrons. Now you will turn those definitions into a reliable calculation method for finding all three subatomic particle counts.

This is a high-value exam skill: it can appear as a quick multiple-choice item, a table-completion question, or part of a longer explanation. By the end of this lesson, you should be able to decode any neutral atom written in nuclear notation without mixing up protons, neutrons, and electrons.

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The three rules to know

For an atom written in the form

$${}_Z^A\mathrm{X}$$

the upper-left number $A$ is the mass number, and the lower-left number $Z$ is the atomic number.

Use these three rules:

$$\text{number of protons}=\text{atomic number}$$ $$\text{number of electrons}=\text{atomic number, for a neutral atom}$$ $$\text{number of neutrons}=\text{mass number}-\text{atomic number}$$

The neutron calculation follows directly from the earlier definition:

$$\text{mass number}=\text{protons}+\text{neutrons}$$

Since the atomic number already gives the number of protons, subtracting it from the mass number leaves the number of neutrons.

Why electrons equal protons in a neutral atom

Each proton has a relative charge of $+1$, while each electron has a relative charge of $-1$. A neutral atom has no overall charge, so its positive and negative charges must balance. Therefore, it has equal numbers of protons and electrons.

This equality applies only because the atom is neutral. Later in the course, you will meet ions, which have gained or lost electrons. Their proton count still identifies the element, but their electron count may differ.

Watch Cognito’s concise explanation to see the three rules applied directly to nuclear symbols.

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A dependable exam routine

When you see a nuclear symbol, do not try to calculate everything mentally at once. Extract the two given numbers first, then fill in the particles in a fixed order.

1. Find the atomic number at the lower left.
2. Write that number as the number of protons.
3. Because the atom is neutral, write the same number as the number of electrons.
4. Subtract atomic number from mass number to find the neutrons.
5. Check that protons plus neutrons add back to the mass number.

Here is the method with aluminium:

$${}_{13}^{27}\mathrm{Al}$$

Particle	Method	Number
Protons	Atomic number	13
Electrons	Same as protons in a neutral atom	13
Neutrons	$27-13$	14

A useful final check is:

$$13+14=27$$

So the calculation is consistent.

Notice that 27 is not the number of neutrons. It is the total of 13 protons and 14 neutrons. This is one of the most common errors in atomic-structure questions.

BBC Bitesize’s Atomic Structure and Writing Formulae presents the same process using sodium. Read it once carefully, concentrating on why each calculation uses a different number.

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Working from numbers given in words

A question will not always give nuclear notation. It may state the atomic number and mass number in a sentence or table. The method remains exactly the same.

Suppose an atom of phosphorus has:

• atomic number $15$
• mass number $31$

The particle counts are:

$$\text{protons}=15$$ $$\text{electrons}=15$$ $$\text{neutrons}=31-15=16$$

The chemical symbol is useful for identifying the element, but it is the two numbers that determine the particle counts.

A compact working layout can make your answers very clear:

Given	Calculation	Answer
Atomic number $=15$	Protons $=15$	15 protons
Neutral atom	Electrons $=15$	15 electrons
Mass number $=31$	Neutrons $=31-15$	16 neutrons

For a short-answer exam question, show the subtraction for neutrons. Even if you make a small arithmetic slip, clear working may help you identify and fix it before moving on.

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Reading chlorine atoms accurately

The two chlorine atoms below have the same atomic number but different mass numbers.

For chlorine-35:

$${}_{17}^{35}\mathrm{Cl}$$ $$\text{protons}=17$$ $$\text{electrons}=17$$ $$\text{neutrons}=35-17=18$$

For chlorine-37:

$${}_{17}^{37}\mathrm{Cl}$$ $$\text{protons}=17$$ $$\text{electrons}=17$$ $$\text{neutrons}=37-17=20$$

The important pattern is that both atoms remain chlorine because both have 17 protons. The difference in mass number comes entirely from the different neutron counts. In the next lesson, this pattern will lead directly to the idea of isotopes.

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Avoiding the exam traps

Do not subtract in the wrong order

The mass number is the larger total, so it comes first:

$$\text{neutrons}=\text{mass number}-\text{atomic number}$$

For calcium-40, with atomic number 20:

$$40-20=20$$

Writing $20-40$ would give an impossible negative neutron number.

Do not include electrons in the mass number

The mass number counts only particles in the nucleus:

• protons
• neutrons

Electrons are outside the nucleus and are not included.

Read what the question is asking about

An atom includes protons, neutrons, and electrons.

A nucleus contains only protons and neutrons. If a question asks for “the particles in the nucleus,” electrons should not appear in your answer.

For example, the nucleus of

$${}_{11}^{23}\mathrm{Na}$$

contains 11 protons and 12 neutrons. The whole neutral sodium atom also has 11 electrons.

Do not use a decimal periodic-table value as a mass number

A mass number is always a whole number because it counts particles in one atom. A periodic table may show a decimal relative atomic mass, such as $35.5$ for chlorine. That value is not itself the mass number of one particular chlorine atom.

For this lesson, use the explicit whole-number mass number supplied in nuclear notation or in the question.

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A fast recall check for revision

Before an exam, write this three-line template from memory:

$$p=Z$$ $$e=Z\text{ for a neutral atom}$$ $$n=A-Z$$

Then briefly check the meaning behind it:

• $Z$ identifies the element because it is the proton count.
• $A$ counts all protons and neutrons in the nucleus.
• Neutrality makes electron number equal proton number.

This takes less than a minute and is more effective than simply rereading the formulas, because it practises retrieving them under pressure.

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Key takeaways

For a neutral atom:

$$\text{protons}=\text{atomic number}$$ $$\text{electrons}=\text{atomic number}$$ $$\text{neutrons}=\text{mass number}-\text{atomic number}$$

Always read the lower-left number as the atomic number and the upper-left number as the mass number. Check your answer by adding protons and neutrons: their total must equal the mass number.

Next, you will use these calculations to decide whether two atoms are isotopes of the same element.