A = N + Z Calculations

You already know how to find the mass number of an isotope by adding the protons and neutrons. We can state the relationship between protons, neutrons, and mass number with the following equation:

A = N + Z

atomic mass number = number of neutrons + atomic number (number of protons)

Atomic mass number will be a whole number. This is different from the average atomic mass listed on the periodic table, which often includes decimals.

Exercise: Complete the chart using a periodic table, as needed.

Element Symbol	Atomic Number	Mass Number	Protons	Neturons
	12	25
Sn		112
			8	9
Au				118
	1			0

Sometimes you do not have enough information to complete the chart. In this case round the average atomic mass from the periodic table to the nearest whole number and use this as the mass number.

Exercise: How many neutrons does Phosphorous (P) have? Note: the average atomic mass for Phosphorus from the Periodic Table is 30.97. Show Answer Answer: Here we round the average atomic mass from the periodic table to a whole number. For Phosphorus, 30.97 becomes 31, which represents the mass number for the most common isotope of Phosphorous. To find neutrons we use A = N + Z. Here 31 = 15 + x. Solving for x we get 16, which is the number of neutrons for the Phosphorous isotope with a mass number of 31 (called Phosphorous-31 or P-31).

What is the difference between mass number, atomic mass, and average atomic mass?

• Mass Number is the number of protons and neutrons in an isotope. This is a whole number. We use the mass number in naming isotopes, like Carbon-12 or Oxygen-17.
• Atomic Mass is the mass of the entire atom of an isotope. This includes electrons as well as a slight change in mass due to binding energy.
• Average Atomic Mass is the weighted average of the isotopes for an element. This is listed below the element symbol on the Periodic Table. It is sometimes called Atomic Weight.