In this explainer, we will learn how to define and calculate the atomic numbers and mass numbers of different atoms.

Atoms consist of protons, neutrons, and electrons. The protons and neutrons, collectively referred to as nucleons, are found in the atom’s nucleus, while the electrons are found in the electron cloud around the nucleus.

### Definition: Nucleons

It is a term that collectively refers to protons and neutrons.

The figure below represents an atom of boron that has five protons, six neutrons, and five electrons.

While a diagram of the atom can easily show the number of each subatomic particle and its general location, there are other ways to represent this information. Nuclide notation or AZE notation () is one such method. The general form for nuclide notation is shown below.

In nuclide notation, represents the chemical symbol of the element as it appears on the periodic table. For example, is the chemical symbol of calcium and is the chemical symbol of silver.

The in nuclide notation represents the atomic number. The atomic number can be used to distinguish one element from another, as each element has its own unique atomic number. This value is frequently written above the element symbol on the periodic table.

The atomic number also indicates the number of protons in the nucleus of all atoms, ions, and isotopes of the element. For example, all atoms of magnesium will have 12 protons in their nucleus, all ions of copper will have 29 protons in their nucleus, and all isotopes of bromine will have 35 protons in their nucleus.

The in nuclide notation represents the mass number: the total number of nucleons in a nucleus of an atom, ion, or isotope.

### Equation: Calculating the Mass Number of an Atom

The following formula can be used to calculate the mass number of an atom:

The mass number is not unique to the element. This means that atoms, isotopes, and ions of a particular element may have different mass numbers. It is also important to recognize that the mass, as reported on the periodic table, is the relative atomic mass.

The relative atomic mass is a weighted average of the masses of each isotope of the element. While the relative atomic mass and mass number may be close in value, they are not interchangeable.

### Example 1: Converting from the Mass Number and the Atomic Number to the Number of Neutrons

An atom of calcium has a mass number of 42 and an atomic number of 20. How many neutrons are there in its nucleus?

### Answer

The atomic number represents the number of protons in the nucleus of all atoms, isotopes, and ions of the element. Therefore, an atom of calcium with an atomic number of 20 has 20 protons in its nucleus.

The mass number is the total number of nucleons in the nucleus of an atom, isotope, or ion. The term *nucleons* collectively
refers to protons and neutrons. The following equation can be used to calculate the mass number:

We have already established that an atom of calcium contains 20 protons. We can substitute the number of protons and the mass number given in the question into the mass number equation and solve for the number of neutrons:

An atom of calcium has 22 neutrons in its nucleus.

Using our understanding of atomic number and mass number, we can represent an atom of boron that contains five protons, six neutrons, and five electrons with the following nuclide notation.

### Example 2: Deducing the Number of Protons and Neutrons and the Mass Number from Nuclide Notation

The isotope oxygen-18 has the nuclide symbol .

- How many protons are there in atoms of oxygen-18?
- How many neutrons are there in atoms of oxygen-18?
- What is the mass number of oxygen-18?

### Answer

**Part 1**

In nuclide notation, the bottom-left number is the atomic number. The atomic number represents the number of protons in the nucleus of an atom, isotope, or ion of the element. Therefore, all atoms of oxygen-18 have eight protons.

**Part 2**

In nuclide notation, the top-left number is the mass number. The mass number is the total number of nucleons in the nucleus of an atom,
isotope, or ion. The term *nucleons* collectively refers to protons and neutrons. The following equation can be used to calculate the
mass number:

We have already established that an atom of oxygen-18 contains eight protons. We can substitute the number of protons and the mass number into the mass number equation and solve for the number of neutrons:

All atoms of oxygen-18 contain 10 neutrons.

**Part 3**

In nuclide notation, the top-left number is the mass number. The mass number is the total number of nucleons in the nucleus of an atom, isotope, or ion. The mass number of oxygen-18 is 18.

Nuclide notation is frequently simplified by omitting the atomic number, as this value can easily be determined using a periodic table. Thus, the simplified nuclide notation of a boron atom containing five protons, six neutrons, and five electrons would be

We can also refer to this boron atom by writing the chemical name followed by a dash and the mass number. For example, we could refer to this atom of boron as boron-11.

### Example 3: Calculating the Atomic Number from an Algebraic Expression in terms of the Mass Number and Deducing the Number of Neutrons

The atomic number of helium-4 is half its mass number. How many neutrons are there in an atom of helium-4?

### Answer

In the notation helium-4, the number four represents the mass number of this atom of helium. If the atomic number of helium-4 is half of its mass number, then the atomic number of helium is two.

The atomic number represents the number of protons in the nucleus of all atoms, isotopes, and ions of the element. Therefore, an atom of helium, which has an atomic number of two, has two protons in its nucleus.

In order to determine the number of neutrons, we need to recognize that the mass number is the total number of nucleons in the
nucleus of an atom, isotope, or ion. The term *nucleons* collectively refers to protons and neutrons. The following equation can
be used to calculate the mass number:

We can substitute the number of protons and the mass number into the mass number equation and solve for the number of neutrons:

An atom of helium-4 has two neutrons in its nucleus.

Nuclide notation provides information regarding the number of protons and neutrons in a nucleus of an atom, isotope, or ion. Nuclide notation can also allow us to determine the number of electrons in an atom. As atoms are neutrally charged, the number of positively charged protons must equal the number of negatively charged electrons.

### Example 4: Reading Number of Electrons, Protons, and Neutrons from Atomic Number and Mass Number

A carbon atom has an atomic number of 6 and a mass number of 12.

- How many protons are there in an atom of carbon?
- How many neutrons are there in an atom of carbon?
- How many electrons are there in an atom of carbon?

### Answer

**Part 1**

The atomic number, frequently represented on the periodic table above the chemical symbol of each element, represents the number of protons in the nucleus of an atom, isotope, or ion of the element. Therefore, a carbon atom that has an atomic number of six has six protons.

**Part 2**

The mass number is the total number of nucleons in the nucleus of an atom, isotope, or ion. The term *nucleons* collectively
refers to protons and neutrons. The following equation can be used to calculate the mass number:

We have already established that an atom of carbon contains six protons. We can substitute the number of protons and the mass number into the mass number equation and solve for the number of neutrons:

This atom of carbon has six neutrons.

**Part 3**

An atom of any element is neutrally charged. To be neutrally charged, the number of positively charged protons must equal the number of negatively charged electrons. The carbon atom contains six protons. Therefore, it must have six electrons to be neutrally charged.

In an ion, the number of protons and that of electrons are not equal. This results in the ion having an overall net charge. The charge of an ion can be calculated by subtracting the number of electrons from the number of protons.

### Equation: Calculating the Charge of an Ion

The following formula can be used to calculate the charge of an ion:

When writing a charge, the numerical value should come first and then the sign. For example, a charge of positive two should be written as 2.

We can include the charge of an ion by writing the charge as a superscript value following the element symbol.

For example, a sodium ion contains 12 neutrons and 10 electrons. Looking at the periodic table, we see that the element sodium has an atomic number of 11. This means that this sodium ion will contain 11 protons. The nuclide notation for this sodium ion would be written as follows.

### Example 5: Determining the Number of Protons, Neutrons, and Electrons in an Ion from the Nuclide Notation

An ion of copper has the nuclide notation .

- How many protons are there in this ion of copper?
- How many neutrons are there in this ion of copper?
- How many electrons are there in this ion of copper?

### Answer

**Part 1**

In nuclide notation, the bottom-left number is the atomic number. The atomic number represents the number of protons in the nucleus of an atom, isotope, or ion of the element. Therefore, with an atomic number of 29, this ion of copper has 29 protons.

**Part 2**

In nuclide notation, the top-left number is the mass number. The mass number is the total number of nucleons in the nucleus
of an atom, isotope, or ion. The term *nucleons* collectively refers to protons and neutrons. The following equation can
be used to calculate the mass number:

We have already established that this ion of copper has 29 protons. We can substitute the number of protons and the mass number into the mass number equation and solve for the number of neutrons:

This ion of copper has 36 neutrons.

**Part 3**

The number written in the top-right corner represents the charge of the ion. The charge of an ion can be calculated using the following equation:

We can substitute the charge and number of protons into the equation and solve for the number of electrons:

This ion of copper has 27 electrons.

### Key Points

- Nuclide notation, , can be used to represent the atomic number and mass number of an atom, isotope, or ion.
- The symbol represents the mass number: the total number of nucleons.
- The symbol represents the atomic number: the number of protons in the nucleus.
- In an atom, the atomic number also indicates the number of electrons in the electron cloud.
- The charge of an ion can be calculated by subtracting the number of electrons from the number of protons.