# Lesson Explainer: Isotopes Physics • 9th Grade

In this explainer, we will learn how to work out the number of protons, neutrons, and electrons an atom of an isotope has from its chemical symbol.

The nucleus of an atom contains protons and neutrons. All atoms of a given element have the same number of protons in their nucleus. The number of protons is represented by the atomic number.

### Definition: Atomic Number

Atomic number is the number of protons in the nucleus of an atom.

Therefore, all atoms of oxygen have eight protons and all atoms of boron have five protons. However, all atoms of a given element do not necessarily have the same number of neutrons in their nucleus.

If we were to sample all the atoms of boron that naturally occur, we would find two types of boron atoms, shown below.

At first glance, these atoms appear to be the same; however, the atom on the left contains six neutrons, whereas the atom on the right contains five neutrons. Atoms that contain the same number of protons but a different number of neutrons are called isotopes.

### Definition: Isotopes

Isotopes are atoms that have the same number of protons but a different number of neutrons.

### Example 1: Definition of Isotopes

Fill in the blank: Isotopes are atoms with the same number of protons but a different number of .

Atoms that have a different number of protons are different elements. Atoms that have the same number of protons but a different number of electrons are called ions. Atoms that have the same number of protons but a different number of neutrons are called isotopes. We should fill in the blank with the word neutrons.

In addition to having a different number of neutrons, isotopes of an element will also have a different mass number.

### Definition: Mass Number

Mass number is the sum of the protons and neutrons in the nucleus.

We can quickly distinguish between isotopes by representing each isotope using nuclide notation, where the top-left number is the mass number and the bottom-left number is the atomic number.

The letter is the chemical symbol, and the letters and are the mass and atomic numbers. The letter describes the number of protons in the atomic nucleus. The letter describes the total number of both protons and neutrons.

### Example 2: Identifying the Heaviest Isotope

Which of the following isotopes is the heaviest?

Nuclide notation is a shorthand method for showing information about atoms. The following figure shows the nuclide notation for an atom. The letter is the chemical symbol, and the letters and are the mass number and atomic number.

The letter is the atomic number and describes the number of protons in the nucleus. The letter is the mass number and describes the total number of nucleons in the atomic nucleus. Heavy atoms have a high mass number, and lighter atoms have a lower mass number.

The question lists atoms that have different atomic and mass numbers. Choice B is the heaviest atom because it has the highest mass number. The argon isotope is heavier than all other listed choices because it contains forty-four nucleons, while the others have fewer nucleons. Choice B is the correct answer to this question.

Scientists use the following equation to determine the number of neutrons in the nucleus of an atom.

### Equation: Number of Neutrons in an Isotope

Let us consider some representative examples to understand the structure of an isotope and how to determine its number of neutrons. We can consider the naturally occurring isotopes of carbon. We will consider carbon-12 first and then carbon-13 and carbon-14. The following nuclide notation describes the carbon-12 isotope.

You will notice that carbon has the C chemical symbol, and carbon-12 has atomic and mass numbers of 6 and 12. Carbon-12 has an atomic number of six because it has six protons. We can determine its number of neutrons by subtracting the number 6 from the number 12. The following equation shows how to determine the number of neutrons in the carbon-12 isotope.

The first line sets up the mathematical equation:

The second line has numerical values in place of the and variables:

The last line shows the result of subtracting the number 6 from the number 12:

It is clear that carbon-12 has six protons and six neutrons. Let us now use the same approach to determine the number of nucleons in the carbon-13 and carbon-14 isotopes. The following table describes the number of nucleons within these two isotopes of the carbon element.

IsotopeNuclear NotationNumber of Protons ()Number of Neutrons ()
carbon-1367
carbon-1468

You will notice that all carbon isotopes have six protons but not the same number of neutrons. One naturally occurring isotope has six neutrons, and the other two have either seven or eight neutrons. You should also notice the use of hyphen notation to describe the isotopes of an element. Hyphen notation has the mass number connected to an element name through a single hyphen. One carbon isotope has the carbon-12 hyphen notation, and the other naturally occurring isotopes have the carbon-13 and carbon-14 hyphen notation.

### Example 3: Identifying Another Isotope of Helium

An atom has 2 protons and 2 neutrons in its nucleus. Which of the following is an isotope of this atom?

1. An atom with no protons and 2 neutrons in its nucleus
2. An atom with 2 protons and 3 neutrons in its nucleus
3. An atom with 1 proton and 2 neutrons in its nucleus
4. An atom with 2 protons and 2 neutrons in its nucleus
5. An atom with 1 proton and 3 neutrons in its nucleus

All atoms of an element have the same number of protons because they have the same atomic number. Helium atoms all have two protons because they all have an atomic number of two. All helium atoms must have two protons, but they can have a different number of neutrons. One helium isotope might have two neutrons, and another could have a higher or lower number of neutrons.

The question describes a helium isotope that has two neutrons. We must identify another helium isotope from the listed choices. Choices B and C are both isotopes of helium, but only B is a different isotope. Choice B is a helium atom with a different number of neutrons. Choice C is the same isotope described in the question and so is incorrect. Choice B is the correct answer to this question.

The mass of an atom is determined from the nuclide notation of an isotope because subatomic particles have one mass that does not change. The following table describes the mass of subatomic particles in an atom of an element.

 Subatomic Particle mass (kg) Electron Proton Neutron 9.11Γ10ο±ο©ο§ 1.67Γ10ο±ο¨ο­ 1.67Γ10ο±ο¨ο­

Protons and neutrons have essentially the same mass ( kg), and an electron is more than one thousand times lighter. Scientists determine the mass of an atom by summing the mass of all protons and neutrons in the atomic nucleus. They usually ignore the mass of all electrons because the mass of an electron is essentially negligible.

### Example 4: Identifying Which System Has the Lowest Mass

Which of the following has the smallest mass?

1. An electron
2. A proton
3. A nucleus
4. A neutron
5. An atom

The atom is a positively charged nucleus with surrounding negatively charged electrons. Mass is distributed unevenly in an atom. The nucleus contains all the protons and neutrons, and the surrounding space contains the low-mass electrons. Protons and neutrons have essentially the same mass, and this is about 1βββ800 times greater than the mass of a single electron.

We can use this background information to determine the correct answer to this question. The background information suggests that the correct answer is either A, B, or D because these are subatomic particles rather than a nucleus or an atom. We can go further and conclude that choice A must be correct because an electron is more than 1βββ000 times lighter than either a proton or neutron. The electron is the lightest subatomic particle in an atom. Choice A is the correct answer to this question.

Let us determine the mass of a single atom of the nitrogen-14 isotope. We first determine that the atom has seven protons and electrons because nitrogen has atomic number seven. We then determine that nitrogen-14 has seven neutrons because when equals 14 and equals 7. We can now set up an equation to determine the mass of a single nitrogen-14 atom:

The symbol is the mass of a single proton. The and symbols are the masses of a single neutron and a single electron respectively. We can discount the negligible mass of all electrons and simplify the equation as follows:

The mass of the atom is the sum of the mass of all protons and neutrons in the atomic nucleus. The following equation has numerical values in place of the and symbols.

You will notice that the mass for a single atom of the nitrogen-14 isotope equals the mass of seven protons and seven neutrons:

The equation can alternatively be stated as follows because the mass of a neutron equals the mass of a proton. The mass of a single atom of nitrogen-14 is simply the total mass of fourteen protons or neutrons:

The next line has numerical values in place of the or symbols. The calculation gives the mass of a single atom of the nitrogen-14 isotope:

The next line shows the result of this numerical calculation. It is clear that a single atom of nitrogen-14 has a mass of kg. We could similarly determine the mass of an atom in any other isotope. We simply multiply the total number of nucleons by the value kg:

The mass of an atom is always approximately equal to the mass number multiplied by the mass of a single proton.

### Example 5: Identifying the Heaviest Isotope

Which of the following isotopes is the heaviest?

1. Carbon-12
2. Oxygen-16
3. Nitrogen-15
4. Boron-11
5. Fluorine-15

The mass of an atom is approximately equal to its mass number multiplied by the mass of a single proton. This statement is sometimes described with the following equation that uses the symbol to represent the mass of a single proton:

The question lists five isotopes, and we can determine their mass number. The mass number is the numerical value connected to the element name with a hyphen. Carbon-12 has mass number twelve because it has the suffix -12 and oxygen-16 has mass number sixteen because it has the suffix -16. The heaviest isotope is the one with the highest suffix number. Oxygen-16 is the heaviest isotope because it has the highest suffix number and the highest mass number. It has a mass of approximately . Choice B is the correct answer to this question.

We considered isotopes of boron and then isotopes of carbon and a single isotope of nitrogen. We should realize, however, that there are many other elements and isotopes. The following table shows the name of some representative chemical elements. It also shows their chemical symbol and atomic number. You will notice that hydrogen has a single proton because it has an atomic number of one. It has the lowest number of protons, and all naturally occurring hydrogen isotopes have very low mass.

Name of ElementChemical SymbolAtomic Number
Hydrogen1
Sodium11
Boron5
Nitrogen7
Oxygen8
Aluminum13
Chlorine17

Let us summarize what we have learned in this explainer.

### Key Points

• All atoms of a given element have the same number of protons and the same atomic number.
• Isotopes are atoms that have the same number of protons but a different number of neutrons.
• Nuclide notation consists of a chemical symbol () with atomic number () and mass number () on the left-hand side.
• The number of neutrons in an isotope equals the mass number minus the atomic number:
• The mass of an electron is more than one thousand times smaller than the mass of a proton or neutron.
• The mass of a proton is essentially the same as the mass of a neutron.
• The mass of an atom approximately equals its mass number multiplied by the mass of a single proton: