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B3.1 · Relate atomic number, mass number, isotopes, and radioisotopes

Learn to relate atomic number, mass number, isotopes, and radioisotopes through clear examples and targeted practice.

Ontario Grade 11 Chemistry

Matter, Chemical Trends, and Chemical Bonding

How proton and neutron counts describe different forms of an element

Some materials can be detected because they give off radiation. Atoms of the same element can also have different masses. These observations connect to the structure of atoms: atoms have protons and neutrons in a central nucleus, and different atoms can have different numbers of neutrons. This lesson uses those particle counts to explain atomic number, mass number, isotopes, and radioisotopes.

What you will learn

Define atomic number and mass number using the particles in an atom.
Use atomic number to identify an element and determine its proton count.
Relate mass number to the numbers of protons and neutrons.
Explain how isotopes of an element are alike and different.
Identify a radioisotope as an isotope that is unstable and emits radiation.

1. Start with the particles in an atom

A useful starting point is the model of an atom. The nucleus is the small, central part of an atom. It contains protons and neutrons. Electrons are found outside the nucleus. A proton has a positive charge, a neutron has no charge, and an electron has a negative charge.

For this lesson, focus on the nucleus. The number of protons identifies the element. For example, every carbon atom has 6 protons. An atom with 7 protons is nitrogen, not carbon. The element's identity does not change when its neutron count changes.

In an atom with no overall charge, the number of electrons equals the number of protons. That fact can help describe a neutral atom, but it is not what determines the element's identity. The proton count does.

Protons and neutrons are in the nucleus.
An element is identified by its number of protons.
In a neutral atom, electron count equals proton count.

2. Atomic number and mass number

The atomic number, written as

Z

, is the number of protons in an atom's nucleus. It is the same for every atom of one element. The periodic table lists elements in order of increasing atomic number.

The mass number, written as

A

, is the total number of protons and neutrons in one atom's nucleus. It is a whole-number count of particles, not the average mass shown for an element on many periodic tables. To find the neutron count, subtract the atomic number from the mass number.

A chemical symbol can be written with the mass number at the upper left and the atomic number at the lower left. In this form,

X

stands for the element's chemical symbol. The upper number gives the total number of protons and neutrons. The lower number gives the protons. If the lower number is missing, the element can still be identified from its chemical symbol and periodic table.

The notation provides a check: the mass number must be at least as large as the atomic number, because protons are part of the total. The difference between them is the number of neutrons.

A = Z + N

$Z$ gives the proton count.
$A$ gives the total proton and neutron count.
Neutron count equals mass number minus atomic number.

3. Isotopes and radioisotopes

Isotopes are atoms of the same element that have different numbers of neutrons. Because they are the same element, their atoms have the same number of protons and the same atomic number. Since their neutron counts differ, their mass numbers differ.

For example, carbon atoms with 6 protons and 6 neutrons and carbon atoms with 6 protons and 8 neutrons are both carbon. Their mass numbers are 12 and 14. They are different isotopes of carbon. The isotope name can be written as carbon-12 or carbon-14, with the number after the hyphen giving the mass number.

Some isotopes are unstable. An unstable isotope that emits radiation is called a radioisotope. The word “radioisotope” describes both its relationship to other isotopes of the same element and its instability. Not every isotope is a radioisotope. A radioisotope still belongs to its element because its proton count has not changed.

A particle-count model helps keep the relationships clear. Imagine two nuclei labelled with the same element symbol. Give them the same number of protons, but different numbers of neutrons. Their atomic numbers match, while their mass numbers do not. If one of those isotopes is unstable and emits radiation, it is a radioisotope.

Isotopes have the same proton count but different neutron counts.
Isotopes of one element have the same atomic number and different mass numbers.
A radioisotope is an unstable isotope that emits radiation.

4. Read and check isotope information

When reading isotope notation, first identify the element from its symbol or atomic number. Next, read the mass number. Then use the difference between the mass number and atomic number to find the neutron count. This order prevents a common mix-up: the atomic number is not the total number of particles in the nucleus.

For example, if an isotope has atomic number 17 and mass number 37, it has 17 protons. Its neutron count is 20. The element with atomic number 17 is chlorine, so the isotope is chlorine-37. If the atom is neutral, it also has 17 electrons.

Counts of protons, neutrons, and electrons are whole numbers, so no rounding or measurement units are needed. Do not treat the periodic table's average atomic mass as the mass number of a particular isotope. The mass number belongs to a specific atom and counts its protons and neutrons.

Use atomic number to find the element and proton count.
Subtract atomic number from mass number to find neutrons.
Mass number is a whole-number count for a particular isotope.

Worked example

Find the particles and compare isotopes

An atom is written as

^{31}_{15}\mathrm{P}

. Determine its element, number of protons, number of neutrons, and number of electrons if it is neutral. Then compare it with phosphorus-32.

Identify the element and protons
The lower number is the atomic number. Atomic number 15 identifies phosphorus, and it also means the nucleus has 15 protons.
$Z = 15$
Find the neutrons
The upper number is the mass number, which counts protons and neutrons together. Subtract the proton count from the total to find the neutrons.
$N = A - Z = 31 - 15 = 16$
Find the electrons
The question says the atom is neutral. A neutral atom has the same number of electrons as protons, so it has 15 electrons.
$e^- = 15$
Compare the isotopes
Phosphorus-32 has the same atomic number because it is still phosphorus. Its mass number is 32, so it has 17 neutrons. The two atoms are isotopes because they have the same number of protons but different numbers of neutrons.
$N = 32 - 15 = 17$

Answer: The atom is phosphorus-31. It has 15 protons, 16 neutrons, and 15 electrons if neutral. Phosphorus-32 has 15 protons and 17 neutrons. They are isotopes of phosphorus.

Check: For phosphorus-31, the nucleus contains 15 + 16 = 31 protons and neutrons, matching its mass number. For phosphorus-32, 15 + 17 = 32.

Common mistakes and how to avoid them

Treating mass number as the number of neutrons.

Correction: Mass number is protons plus neutrons. Subtract atomic number from mass number to find neutrons.

Saying isotopes of the same element have different atomic numbers.

Correction: They have the same atomic number because they have the same number of protons. Their neutron counts and mass numbers differ.

Assuming every isotope is radioactive.

Correction: A radioisotope is an unstable isotope that emits radiation. The term does not apply to every isotope.

Using the periodic table's average atomic mass as an isotope's mass number.

Correction: Use the whole-number mass number given for the particular isotope. It counts the protons and neutrons in that atom's nucleus.

Lesson summary

Atomic number is the number of protons and identifies the element.
Mass number is the total number of protons and neutrons in one nucleus.
Neutrons equal mass number minus atomic number.
Isotopes have equal proton counts and different neutron counts.
A radioisotope is an unstable isotope that emits radiation.

Check your understanding

Question 1

An atom has atomic number 8 and mass number 18. How many neutrons does it have?

Show answer and explanation

Neutrons equal mass number minus atomic number: 18 - 8 = 10.

Question 2

Which statement describes two isotopes of the same element?

They have the same number of neutrons and different numbers of protons.
They have different numbers of protons and different atomic numbers.
They have the same number of protons and different numbers of neutrons.
They have the same mass number and different numbers of protons.

Show answer and explanation

They have the same number of protons and different numbers of neutrons.

Isotopes remain the same element because their proton counts match. Their neutron counts differ.

Question 3

What makes an isotope a radioisotope?

It has no protons.
It has an unstable nucleus and emits radiation.
It has the same mass number as every other isotope of its element.
It has a different atomic number from other isotopes of its element.

Show answer and explanation

It has an unstable nucleus and emits radiation.

A radioisotope is an unstable isotope that emits radiation. Isotopes of the same element have the same atomic number.

Key terms

Atomic number: The number of protons in an atom's nucleus; it identifies the element.
Mass number: The total number of protons and neutrons in one atom's nucleus.
Isotope: One of two or more forms of the same element with different numbers of neutrons.
Radioisotope: An unstable isotope that emits radiation.
Nucleus: The central part of an atom that contains protons and neutrons.

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Published by DoAssignment. This AI-assisted lesson follows Ontario Grade 11 Chemistry (SCH3U), expectation B3.1. It is a study resource, not an official curriculum publication.

Before publication, the draft is checked for structure, mathematical or chemical notation, calculations, course boundaries, and readability, and then requires administrator approval. Errors can still occur, so corrections are welcomed.

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