How can we determine the number …

This nucleus has 56 protons and 137 − 56 = 81 neutrons.

Explanation:

Two numbers are used to identify a nucleus: Atomic number -- It is number of just protons in the nucleus. The atomic the number of protons determines the number of electrons as number of protons is always equal to number of electrons. Mass number- It is the number of protons plus neutrons. This is roughly proportional to the total mass of the atom. Mass number is also a key property of atoms because we need to know the masses of atoms to understand how a given amount of material we weigh out will react. When the element is barium, that means the aomic number is 56. "barium 137" means 56 protons. And the 137 for the mass number designates 137 total protons plus neutrons. To get just the number of neutrons you take the difference between protons and neutrons, thus 137 − 56 = 81 .