How Do You Find the Number of Neutrons? A Step-by-Step Guide

To find the number of neutrons in an atom, subtract the atomic number from the mass number. The formula is: Neutrons = Mass Number – Atomic Number. The atomic number tells you how many protons are in the nucleus, and the mass number is the total count of protons plus neutrons. This calculation works for any single isotope of an element.

Understanding the Two Key Numbers

Before you do the subtraction, you need to know where to find the atomic number and the mass number.

Atomic Number (Z)

The atomic number is the number of protons in the nucleus. Every atom of a given element has the same number of protons. For example, every carbon atom has 6 protons, so its atomic number is 6. You can find this number on any periodic table, usually displayed above the element symbol. The International Union of Pure and Applied Chemistry (IUPAC) standardizes these values International Union of Pure and Applied Chemistry.

Mass Number (A)

The mass number is the total number of protons and neutrons in the nucleus. Unlike the atomic number, the mass number is not fixed for a given element. Atoms of the same element can have different numbers of neutrons. These different versions are called isotopes.

For instance, the most common isotope of carbon has 6 neutrons, giving it a mass number of 12 (6 protons + 6 neutrons). Another isotope, carbon-14, has 8 neutrons, giving it a mass number of 14. The mass number is usually written as a superscript to the left of the element symbol (e.g., ¹²C or ¹⁴C).

The Step-by-Step Calculation

Once you have the mass number and the atomic number, the calculation is a single subtraction.

1. Identify the element and its isotope. If the problem gives you a specific notation like “oxygen-16” or “¹⁶O,” use that mass number.
2. Find the atomic number. Look up the element on the periodic table. For oxygen, the atomic number is 8.
3. Find the mass number. Use the number provided in the isotope notation. For oxygen-16, the mass number is 16.
4. Subtract. 16 – 8 = 8 neutrons.

Worked Example: Chlorine

Chlorine has an atomic number of 17. It has two stable isotopes: chlorine-35 and chlorine-37.

• For chlorine-35: Neutrons = 35 – 17 = 18 neutrons.
• For chlorine-37: Neutrons = 37 – 17 = 20 neutrons.

The Royal Society of Chemistry provides detailed data on these isotopes in their periodic table Royal Society of Chemistry.

Working with the Periodic Table

Most periodic tables show the atomic number and the average atomic mass, not the mass number of a specific isotope. The average atomic mass is a weighted average of all the isotopes found in nature. It is usually a decimal number (e.g., 35.45 for chlorine).

You cannot use the average atomic mass directly in the “mass number minus atomic number” formula. That formula only works with a whole-number mass number for a specific isotope.

If you only have the periodic table and need an approximate number of neutrons for the most common isotope, round the average atomic mass to the nearest whole number. For chlorine, rounding 35.45 gives you 35. Then, 35 – 17 = 18 neutrons. This is a good estimate, but it is not exact for every atom.

Common Mistakes to Avoid

The most frequent mistake is confusing the atomic number with the mass number. The atomic number is always the smaller of the two, and it is the same for every atom of that element.

Another common error is using the average atomic mass from the periodic table as if it were the mass number. For example, bromine has an average atomic mass of about 79.9. If you subtract its atomic number (35) from 79.9, you get 44.9. That is not a valid number of neutrons. The actual isotopes of bromine are bromine-79 (44 neutrons) and bromine-81 (46 neutrons). The decimal result is meaningless for a single atom.

A third mistake happens when dealing with ions. Ions have a different number of electrons, but the number of protons and neutrons in the nucleus does not change. The formula for neutrons stays the same regardless of the electrical charge of the atom.

Key Takeaways

• The number of neutrons is found by subtracting the atomic number (protons) from the mass number (protons + neutrons).
• The atomic number is unique to each element and is found on the periodic table.
• The mass number is specific to a single isotope and must be a whole number.
• Do not use the average atomic mass from the periodic table for the direct subtraction formula; round it for an estimate of the most common isotope.
• The neutron count determines the isotope, which influences the atom’s stability and its applications in medicine, archaeology, and energy.