ChemGem

How to Find the Number of Neutrons from the Mass Number (Step-by-Step, with Practice)

The mass number counts the particles in one atom’s nucleus: protons plus neutrons. Subtract the protons to get the neutrons.

Spot it, solve it, practice it: 3 steps, 1 worked example, 3 practice problems. Free, no account.

ChemGemUpdated Section 1.2

The route · 3 steps

  1. Find the mass number (A) in the isotope name or notation.
  2. Read the atomic number (Z), the proton count, from the periodic table.
  3. Subtract: neutrons = A − Z.
Try one now See a worked example
Spot it

How to recognize mass number questions

Look for "mass number" or a name like carbon-13 plus a proton count, with neutrons asked for.

Example wording, with the clue words marked:

An isotope has 13 protons and mass number 31. How many neutrons does it have?

Not sure it’s this type? Compare the neighbors:

Step-by-step

Worked example: mass number

The idea

Reading isotope notation
146CMass number, Aprotons + neutronsAtomic number, Zprotons onlySymbolset by Zneutrons = A − Z = 14 − 6 = 8
Mass number upper left, atomic number lower left: 146C.
Neutrons = mass number − protons
n = A − Z
A is the isotope’s whole-number mass number; Z is the proton count.
A lithium-7 atom: 3 protons and 4 neutrons in the nucleus, 3 electrons outside. Mass number = protons + neutrons = 3 + 4 = 7. Electrons are not included.
Lithium-7: 3 + 4 = 7. Electrons do not count.
Isotopes: same element, different neutrons
++++++++++++carbon-126 p + 6 n = 12carbon-146 p + 8 n = 14proton (+)neutron (no charge)same protons, different neutrons
Isotopes: same element, different neutron counts, so different mass numbers. Section 1.4 averages them.
Boron-11 with 5 protons and 6 neutrons, carbon-12 with 6 and 6, and nitrogen-14 with 7 and 7, each with electrons as small dots.
Protons alone decide the element (5, 6, 7). Adding neutrons gives the mass number: 5 + 6 = 11, 6 + 6 = 12, 7 + 7 = 14.
Counting the particles in a neutral atom
IsotopeProtons (Z)Neutrons (A − Z)ElectronsMass number (A)
73Li37 − 3 = 437
115B511 − 5 = 6511
126C612 − 6 = 6612
146C614 − 6 = 8614
147N714 − 7 = 7714
3416S1634 − 16 = 181634
Neutral atom: electrons = protons.

On the periodic table: The whole number in each box is the atomic number, the proton count: lithium (Li) 3, boron (B) 5, carbon (C) 6, nitrogen (N) 7, sulfur (S) 16.

On the periodic table: The mass number comes from the isotope name, not the table. Use supplied masses when a problem gives them.

Worked example · 3 steps

Sulfur-34 has 16 protons. How many neutrons does it have?

3416S
Sulfur-34 in isotope notation.
  1. 1
    Name the total

    The 34 counts all the protons and neutrons together.

    Mass number, A = 34
  2. 2
    Take away the protons

    Removing the protons leaves the neutrons. On the periodic table: sulfur (S) is number 16.

    n = A − Z
    n = 34 − 16
  3. 3
    Do the subtraction

    The result is the neutron count.

    Protons+ Neutrons= Mass number
    161834
  4. ✓
    Answer

    Sulfur-34 has 18 neutrons.

Your turn

Mass number practice problems

Answer first, then check. Hints open one at a time; the answer and full solution open after you try.

Problem 1 of 3 · warm-up

An isotope has 13 protons and mass number 31. How many neutrons does it have?

Hint 1 · the clue

Both mass number and proton count are given.

Hint 2 · the next move

Protons and mass number are given and neutrons are asked for: subtract protons from the mass number.

Your path:

  1. Mass number = protons + neutrons
  2. Neutrons = mass number − protons
  3. Check by adding back
Answer

Answer: 18

Full worked solution

What you know: 13 protons, mass number 31. What you want: the number of neutrons.

  1. Mass number counts protons plus neutrons in one isotope: 31 = 13 + neutrons.
  2. Take the protons away to leave only neutrons: neutrons = 31 − 13 = 18.

Check: Add back: 13 protons + 18 neutrons = 31, the mass number.

Watch out: Use the isotope's whole-number mass number from the problem, not the decimal average mass on the periodic table.

Your route: Mass number → Subtract protons

13Al26.98On the periodic table: An atom with 13 protons is aluminum (Al); you can also read aluminum’s atomic number, 13, from its box. The mass number 31 comes from the problem, not the table.

Answer: 18

Problem 2 of 3

An isotope has 14 protons and mass number 33. How many neutrons does it have?

Hint 1 · the clue

Both mass number and proton count are given.

Hint 2 · the next move

Protons and mass number are given and neutrons are asked for: subtract protons from the mass number.

Your path:

  1. Mass number = protons + neutrons
  2. Neutrons = mass number − protons
  3. Check by adding back
Answer

Answer: 19

Full worked solution

What you know: 14 protons, mass number 33. What you want: the number of neutrons.

  1. Mass number counts protons plus neutrons in one isotope: 33 = 14 + neutrons.
  2. Take the protons away to leave only neutrons: neutrons = 33 − 14 = 19.

Check: Add back: 14 protons + 19 neutrons = 33, the mass number.

Watch out: Use the isotope's whole-number mass number from the problem, not the decimal average mass on the periodic table.

Your route: Mass number → Subtract protons

14Si28.09On the periodic table: An atom with 14 protons is silicon (Si); you can also read silicon’s atomic number, 14, from its box. The mass number 33 comes from the problem, not the table.

Answer: 19

Problem 3 of 3

Carbon-13 has 6 protons. Neutrons?

Hint 1 · the clue

Mass number includes protons and neutrons. Subtract the proton count from the mass number.

Hint 2 · the next move

An isotope name like carbon-13 gives the mass number; with protons given, subtract to find neutrons.

Your path:

  1. Number in the name = mass number
  2. Neutrons = mass number − protons
  3. Don't use the table's decimal mass
Answer

13 − 6 = 7.

Full worked solution

What you know: carbon-13, 6 protons. What you want: the number of neutrons.

  1. The 13 in carbon-13 is the mass number: protons + neutrons = 13.
  2. Subtract the protons: neutrons = 13 − 6 = 7.

Check: 6 protons + 7 neutrons = 13, the mass number.

Watch out: Use the 13 from the isotope name, not carbon's decimal mass (12.01) from the table.

6C12.01On the periodic table: Carbon (C) has atomic number 6, the whole number in its box, so it has 6 protons. The 13 comes from the isotope name, not the table.

Answer: 13 − 6 = 7.

Watch out

Common mass number mistakes