Neutrons Equation: Find Neutrons in an Isotope

Use the neutron equation to find how many neutrons an atom’s isotope contains: subtract its atomic number from its mass number. Enter those two whole-number values to get the neutron count; the result applies to a specific isotope, not just an element.

Formula

The neutron equation is:

N = A − Z

• N is the number of neutrons in one atom’s nucleus, in particles.
• A is the mass number: the total number of protons and neutrons in the nucleus, a whole-number count with no unit.
• Z is the atomic number: the number of protons in the nucleus, also a whole-number count with no unit.

The calculator also displays the proton count, which is equal to Z. The inputs must describe a possible nuclide: the mass number cannot be smaller than the atomic number. If A is less than Z, the subtraction would give an impossible negative neutron count. Check the isotope notation or numbers before using the result.

Worked Example

The default values represent sodium-23: A = 23 and Z = 11.

1. Use N = A − Z.
2. Substitute the inputs: N = 23 − 11.
3. Subtract: N = 12 neutrons.
4. The proton count is Z = 11 protons.

The calculator therefore returns 12 neutrons and 11 protons. The neutron result is the headline answer.

Assumptions

• The inputs are whole-number mass and atomic numbers for one isotope.
• The nuclide is physically and chemically identified correctly; this arithmetic does not determine whether an isotope is stable.
• Electron counts are not included. Electrons are outside the nucleus and do not enter this equation.

What You’ll Need

• The element’s atomic number, found on a periodic table. It is the number of protons.
• The isotope’s mass number, usually shown as a superscript in isotope notation or stated after the element name, such as 23 in sodium-23.
• A calculator is optional; the equation uses a simple subtraction.

Step-by-Step

1. Identify the element. Find its symbol or name in a periodic table and note its atomic number. For example, sodium has atomic number 11. Do not use the element’s average atomic weight as the atomic number.
2. Identify the isotope’s mass number. Look for the whole-number count of protons plus neutrons. In the name carbon-14, the mass number is 14. In isotope notation, the mass number is commonly written at the upper left of the element symbol, as in ¹⁴C.
3. Check that both values are whole numbers. The atomic number counts protons, while the mass number counts protons and neutrons together. A periodic table’s atomic mass is often a decimal because it is a weighted average across naturally occurring isotopes; it is not the mass number for a particular atom.
4. Subtract the atomic number from the mass number. Calculate N = A − Z. For carbon-14, this is 14 − 6 = 8, so each carbon-14 nucleus has 8 neutrons.
5. Check the result. A neutron count must be zero or a positive whole number. Also verify that the mass number is at least as large as the atomic number. If the result is negative or decimal, one or both inputs are wrong or are not the right kind of value.
6. State the isotope with the answer. Write a clear result such as “carbon-14 has 8 neutrons.” The number of neutrons can differ between isotopes of the same element, even though all atoms of that element have the same atomic number.

Common Mistakes

• Using atomic mass in place of mass number. The periodic-table value is generally an average that can be decimal. Use the isotope’s specific whole-number mass number. Rounding an average atomic mass may sometimes suggest a common isotope, but it does not identify the isotope reliably.
• Reversing the subtraction. Subtract protons from the total nucleons: mass number minus atomic number. Reversing the order usually produces a negative answer.
• Confusing neutrons and protons. The atomic number itself is the proton count. It is not the neutron count. Neutrons are the difference between mass number and atomic number.
• Assuming an element has only one neutron count. Isotopes have the same number of protons but different numbers of neutrons. Always use the mass number for the isotope in question.
• Including electrons in the equation. The mass number counts only protons and neutrons in the nucleus. A neutral atom’s electrons do not change the neutron count; neither does an ion’s charge.

Tips

• Remember the relationship as “mass number equals protons plus neutrons”: A = Z + N. Rearranging gives N = A − Z.
• Use a periodic table for Z and an isotope label or nuclide chart for A. Check that the element symbol and isotope name agree.
• For isotope notation such as ²³₁₁Na, the upper-left number is A = 23 and the lower-left number is Z = 11; therefore, N = 12.
• Keep the answer as an integer count. There is no rounding step in this equation.

Troubleshooting

The answer is negative: Confirm that A is the mass number and Z is the atomic number, then check that A is not smaller than Z. Ensure you have not swapped the fields or entered an atomic mass instead of a mass number.

The answer is a decimal: Neutron counts are whole numbers. Replace any decimal atomic weight with the isotope’s mass number, and enter whole-number values for both fields.

You do not know the mass number: The element name alone is not enough to give a unique neutron count because it may have multiple isotopes. Find the isotope designation first. If no isotope is specified, explain that the neutron count cannot be determined uniquely from the element alone.

Your notation has several numbers: In standard isotope notation, use the upper-left superscript for mass number and the lower-left subscript for atomic number. Do not mistake an ion’s charge, often shown at the upper right, for either value.

Frequently Asked Questions

What is the equation for finding neutrons?
Subtract the atomic number from the mass number: N = A − Z.

How do I find the atomic number?
Look up the element on a periodic table. Its atomic number is the number of protons in its nucleus.

Can I use the atomic mass shown on a periodic table?
Not for an exact isotope calculation. Atomic mass is often an average across isotopes, whereas this equation needs the isotope’s whole-number mass number.

How many neutrons does sodium-23 have?
Sodium has atomic number 11, so sodium-23 has 23 − 11 = 12 neutrons.

Can two isotopes have different neutron counts?
Yes. Isotopes of an element have the same number of protons but different numbers of neutrons, which gives them different mass numbers.

Does an ion’s charge affect its neutron count?
No. Losing or gaining electrons changes the charge, not the nucleus. Find neutrons from the isotope’s mass number and atomic number.

Related

• Mole Calculator From a Chemical Equation: Moles of Product From the Mole Ratio
• Percent Yield Calculator: Actual Yield ÷ Theoretical Yield × 100

in a | Mass number A | - | 23 | 1
in z | Atomic number Z | - | 11 | 1
out n | Neutrons | particles | a - z | 0
out p | Protons | particles | z | 0