Mass Number: How to Calculate Neutrons, Protons and Electrons

“How many neutrons does this atom have?” is one of the first calculation questions in chemistry, and one of the easiest marks to win, once you know the method. This article explains mass number, shows how it connects to atomic number, and then works through examples of steadily increasing difficulty, including isotopes and ions.

The two key numbers

• Atomic number (Z): the number of protons. It identifies the element. See atomic number explained.
• Mass number (A): the total number of protons + neutrons (together called nucleons) in the nucleus.

Electrons aren’t counted in the mass number because their mass is tiny, about 1/1836 of a proton’s.

From these, everything else follows:

To find…	Use
protons	= Z
neutrons	= A − Z
electrons (neutral atom)	= Z
electrons (ion)	= Z − charge (for positive ions, subtract; for negative ions, add)

Nuclide notation

Atoms are often written with the mass number as a superscript and the atomic number as a subscript, both on the left of the symbol:

ᴬ_Z X — for example, ²³₁₁Na (sodium-23) or ³⁵₁₇Cl (chlorine-35).

You’ll also see the name–mass form: sodium-23, chlorine-35, carbon-14. Here only the mass number is given, because the element name already tells you Z. See how to read and write isotope notation.

Worked examples: neutral atoms

Example 1: sodium-23 (Z = 11)

• Protons = 11
• Neutrons = 23 − 11 = 12
• Electrons = 11

Example 2: ⁵⁶₂₆Fe

• Protons = 26
• Neutrons = 56 − 26 = 30
• Electrons = 26

Example 3: uranium-238 (Z = 92)

• Protons = 92
• Neutrons = 238 − 92 = 146
• Electrons = 92

Example 4: hydrogen-1 (Z = 1)

• Protons = 1
• Neutrons = 1 − 1 = 0
• Electrons = 1

Ordinary hydrogen is the only stable atom with no neutrons.

Worked examples: isotopes

Isotopes of an element have the same Z (same protons) but different A (different neutrons).

Example 5: the three isotopes of carbon

Isotope	Protons	Neutrons	Electrons
carbon-12	6	6	6
carbon-13	6	7	6
carbon-14	6	8	6

Carbon-14 is radioactive and is used in carbon dating.

Example 6: chlorine-35 and chlorine-37 (Z = 17)

• Cl-35: 17 protons, 18 neutrons, 17 electrons
• Cl-37: 17 protons, 20 neutrons, 17 electrons

Chemically they behave the same, because they have the same number of electrons. See isotopes, ions, isomers and allotropes.

Worked examples: ions

An ion’s charge comes from an imbalance between protons and electrons. The nucleus doesn’t change, so protons and neutrons stay the same as in the atom.

• Positive ion (cation): has lost electrons. Electrons = Z − charge.
• Negative ion (anion): has gained electrons. Electrons = Z + size of charge.

Example 7: ²⁴₁₂Mg²⁺

• Protons = 12
• Neutrons = 24 − 12 = 12
• Electrons = 12 − 2 = 10

Example 8: ³²₁₆S²⁻

• Protons = 16
• Neutrons = 32 − 16 = 16
• Electrons = 16 + 2 = 18

Example 9: ²⁷₁₃Al³⁺

• Protons = 13
• Neutrons = 27 − 13 = 14
• Electrons = 13 − 3 = 10

Notice that Mg²⁺, Al³⁺ and also Na⁺, F⁻ and O²⁻ all have 10 electrons: the same electron arrangement as neon. They’re isoelectronic. See what is an ion?

Working backwards

Example 10: An atom has 35 protons and 45 neutrons. Identify it and write its symbol.

• Z = 35 → bromine
• A = 35 + 45 = 80
• Symbol: ⁸⁰₃₅Br (bromine-80)

Example 11: An ion has 29 protons, 34 neutrons and 27 electrons. Identify it.

• Z = 29 → copper
• A = 29 + 34 = 63
• Charge = 29 − 27 = +2
• Symbol: ⁶³₂₉Cu²⁺

Example 12: A particle has mass number 40 and 18 electrons, and a charge of 2+. How many neutrons does it have?

• Charge 2+ means protons = electrons + 2 = 20 → Z = 20 (calcium)
• Neutrons = 40 − 20 = 20

Mass number vs relative atomic mass

Students often confuse these.

	Mass number (A)	Relative atomic mass (Aᵣ)
Refers to	one specific isotope	the element as found in nature
Value	always a whole number	usually not a whole number
Example (chlorine)	35 or 37	35.45
Where you find it	in nuclide notation	on the periodic table

Relative atomic mass is a weighted average of the masses of an element’s isotopes. Chlorine is about 76% chlorine-35 and 24% chlorine-37, giving 35.45. See calculating relative atomic mass from isotope abundances and atomic mass vs mass number vs molar mass.

Don’t calculate neutrons by subtracting Z from the relative atomic mass on the periodic table unless the question tells you to use the most common isotope. For chlorine, 35.45 − 17 = 18.45 neutrons makes no sense, because atoms can’t have fractional neutrons.

Why mass number is useful

Mass number is more than a counting exercise. It lets you:

• Tell isotopes apart in medicine and industry, where the difference between, say, iodine-127 (stable) and iodine-131 (radioactive, used to treat thyroid conditions) matters enormously.
• Balance nuclear equations, where the total mass number must be the same on both sides. See how to read and write isotope notation.
• Estimate the mass of an atom: an atom’s mass in atomic mass units is close to its mass number, because protons and neutrons each have a mass of about 1 u and electrons contribute very little. Sodium-23 has a mass of about 23 u.
• Understand nuclear stability: light stable nuclei have roughly equal numbers of protons and neutrons (carbon-12 has 6 and 6), while heavy stable nuclei have more neutrons than protons (lead-208 has 82 protons and 126 neutrons). The extra neutrons help dilute the repulsion between the many positively charged protons.

A quick method for exam questions

When a question gives you an atom or ion, write a three-row mini table before doing anything else:

Protons	Neutrons	Electrons
Z	A − Z	Z − charge

Filling in the rows in this order, protons first, avoids the most common mix-ups. Remember that for a negative charge, “minus the charge” means adding electrons: for a 2− ion, electrons = Z − (−2) = Z + 2.

Practice questions

1. How many neutrons are in potassium-39 (Z = 19)?
2. How many electrons are in ¹⁹F⁻ (Z = 9)?
3. An atom has 47 protons and 60 neutrons. Write its symbol.
4. How many protons, neutrons and electrons are in ⁵²Cr³⁺ (Z = 24)?
5. Which two of these are isotopes of the same element: ⁴⁰₁₈X, ⁴⁰₂₀Y, ⁴²₂₀Z?

Answers:

1. 39 − 19 = 20
2. 9 + 1 = 10
3. Z = 47 is silver; A = 107 → ¹⁰⁷₄₇Ag
4. 24 protons, 28 neutrons, 21 electrons
5. Y and Z (both Z = 20, calcium). X and Y have the same mass number but are different elements (argon and calcium); such atoms are called isobars.

Common mistakes

• Adding electrons to the mass number.
• Changing the number of protons when forming an ion (only electrons change).
• Getting the direction wrong for ions: negative ions have more electrons than protons.
• Using relative atomic mass instead of mass number.
• Swapping A and Z in nuclide notation. The bigger number is always the mass number (except for hydrogen-1, where both are 1).

Key takeaways

• Mass number (A) = protons + neutrons; atomic number (Z) = protons.
• Neutrons = A − Z.
• In a neutral atom, electrons = Z; in an ion, subtract a positive charge or add a negative charge.
• Isotopes have the same Z but different A; ions have the same nucleus but different numbers of electrons.
• Mass number is a whole number for one isotope; relative atomic mass is a weighted average for the element.