Atomic Nuclei and Radioactivity

What Is an Isotope?

Every element is defined by the number of protons in its nucleus.

For example:

• Hydrogen always has 1 proton.
• Carbon always has 6 protons.
• Oxygen always has 8 protons.
• Chlorine always has 17 protons.

However, atoms of the same element do not always contain the same number of neutrons.

Atoms that have the same number of protons but different numbers of neutrons are called isotopes.

So the key definition is:

Isotopes are atoms of the same element with the same number of protons but different numbers of neutrons.

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What Stays the Same in Isotopes?

Isotopes of the same element must have the same number of protons.

This is because the number of protons determines the identity of an element.

For example, every carbon atom contains:

6 protons

If a nucleus had 7 protons instead, it would no longer be carbon. It would be nitrogen.

Therefore, different isotopes of carbon all have:

Atomic number = 6

What changes between the isotopes is the number of neutrons.

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What Is Different in Isotopes?

Consider three common isotopes of carbon:

Carbon-12

• Protons = 6
• Neutrons = 6
• Nucleon number = 12

Carbon-13

• Protons = 6
• Neutrons = 7
• Nucleon number = 13

Carbon-14

• Protons = 6
• Neutrons = 8
• Nucleon number = 14

All three atoms are carbon because they contain 6 protons.

However, they have different numbers of neutrons and therefore different masses.

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Why Do Isotopes Have Different Masses?

Protons and neutrons have approximately the same mass.

Electrons have much less mass than either protons or neutrons.

Therefore, most of the mass of an atom comes from the particles in its nucleus.

If two isotopes have different numbers of neutrons, they contain different numbers of nucleons.

This means they have different masses.

For example:

Carbon-12 → 6 protons + 6 neutrons = 12 nucleons

Carbon-14 → 6 protons + 8 neutrons = 14 nucleons

Carbon-14 therefore has a greater mass than carbon-12.

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Atomic Number

The atomic number is the number of protons in the nucleus.

It is sometimes represented by the symbol Z.

Therefore:

Atomic number = number of protons

For example:

Oxygen has atomic number 8.

Every isotope of oxygen therefore contains:

8 protons

The number of neutrons can change, but the proton number cannot change without producing a different element.

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Nucleon Number

The nucleon number, also called the mass number, is the total number of protons and neutrons in the nucleus.

Therefore:

Nucleon number = protons + neutrons

It is often represented by the symbol A.

For example, an atom containing:

• 8 protons
• 10 neutrons

has:

Nucleon number = 8 + 10 = 18

Because it contains 8 protons, it is oxygen.

Therefore, this isotope is oxygen-18.

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Finding the Number of Neutrons

The number of neutrons can be calculated using:

Neutrons = nucleon number − atomic number

For example, sodium-23 has:

Atomic number = 11

Nucleon number = 23

Therefore:

Neutrons = 23 − 11

Neutrons = 12

So sodium-23 contains:

• 11 protons
• 12 neutrons

If the atom is neutral, it also contains 11 electrons.

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Isotope Names

One simple way of identifying an isotope is to write the name of the element followed by its nucleon number.

Examples include:

• Carbon-12
• Carbon-13
• Carbon-14
• Hydrogen-1
• Hydrogen-2
• Hydrogen-3
• Oxygen-16
• Oxygen-17
• Oxygen-18
• Uranium-235
• Uranium-238

The number after the element name is the nucleon number, not the atomic number.

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Isotope Notation

Isotopes can also be represented using nuclear notation.

For example:

¹²₆C

The symbol C identifies the element as carbon.

The upper number, 12, is the nucleon number.

The lower number, 6, is the atomic number.

Therefore:

Protons = 6

Neutrons = 12 − 6 = 6

Another carbon isotope is:

¹⁴₆C

This contains:

Protons = 6

Neutrons = 14 − 6 = 8

The two atoms are isotopes because they have the same proton number but different neutron numbers.

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Worked Example: Magnesium-26

Consider:

²⁶₁₂Mg

The atomic number is 12.

Therefore:

Protons = 12

The nucleon number is 26.

Calculate the number of neutrons:

Neutrons = 26 − 12

Neutrons = 14

So magnesium-26 contains:

• 12 protons
• 14 neutrons
• 12 electrons if the atom is neutral

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Worked Example: Identifying an Isotope

An atom contains:

• 17 protons
• 20 neutrons

The atomic number is therefore:

17

Atomic number 17 corresponds to chlorine.

The nucleon number is:

17 + 20 = 37

Therefore, the isotope is:

Chlorine-37

Its isotope notation is:

³⁷₁₇Cl

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Comparing Two Isotopes

Consider:

³⁵₁₇Cl

and:

³⁷₁₇Cl

For chlorine-35:

Protons = 17

Neutrons = 35 − 17 = 18

For chlorine-37:

Protons = 17

Neutrons = 37 − 17 = 20

Both atoms contain 17 protons, so both are chlorine.

However, they contain different numbers of neutrons.

Therefore, chlorine-35 and chlorine-37 are isotopes of chlorine.

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The Isotopes of Hydrogen

Hydrogen provides a particularly useful example because its three well-known isotopes have special names.

Hydrogen-1: Protium

Hydrogen-1 contains:

• 1 proton
• 0 neutrons

It is the most common isotope of hydrogen.

Hydrogen-2: Deuterium

Hydrogen-2 contains:

• 1 proton
• 1 neutron

It is also called deuterium.

Hydrogen-3: Tritium

Hydrogen-3 contains:

• 1 proton
• 2 neutrons

It is also called tritium and is radioactive.

All three are hydrogen because they all contain exactly one proton.

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Common Isotopes of Carbon

Carbon has several isotopes, including carbon-12, carbon-13, and carbon-14.

Carbon-12

• 6 protons
• 6 neutrons
• Stable

Carbon-13

• 6 protons
• 7 neutrons
• Stable

Carbon-14

• 6 protons
• 8 neutrons
• Radioactive

Carbon-14 is particularly useful because it can be used to estimate the age of once-living materials.

This technique is known as radiocarbon dating.

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Common Isotopes of Oxygen

Naturally occurring oxygen includes several isotopes.

Oxygen-16

• 8 protons
• 8 neutrons

Oxygen-17

• 8 protons
• 9 neutrons

Oxygen-18

• 8 protons
• 10 neutrons

All are oxygen because they contain 8 protons.

Oxygen-16 is by far the most abundant of these naturally occurring isotopes.

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Uranium Isotopes

Two important naturally occurring uranium isotopes are:

Uranium-235

and:

Uranium-238

Uranium has atomic number 92.

Therefore, both isotopes contain:

92 protons

Uranium-235 contains:

235 − 92 = 143 neutrons

Uranium-238 contains:

238 − 92 = 146 neutrons

Both are uranium, but their nuclear properties are different.

Uranium-235 is particularly important because it can undergo nuclear fission in ways that make it useful as fuel in many nuclear reactors.

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Stable and Radioactive Isotopes

Not all isotopes are stable.

A stable isotope has a nucleus that does not spontaneously undergo radioactive decay.

Examples include:

• Carbon-12
• Carbon-13
• Oxygen-16

A radioactive isotope, or radioisotope, has an unstable nucleus that can undergo radioactive decay.

Examples include:

• Hydrogen-3
• Carbon-14
• Uranium-235
• Uranium-238

The stability of a nucleus depends on several factors, including the numbers and arrangement of protons and neutrons.

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Do Isotopes Have the Same Chemical Properties?

Isotopes of the same element generally have very similar chemical properties.

This is because chemical behaviour is mainly determined by the arrangement of electrons.

Neutral isotopes of the same element have:

• The same number of protons
• The same number of electrons
• The same electron arrangement

Therefore, their chemical behaviour is usually very similar.

However, their masses and nuclear properties can differ.

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Isotopes and Relative Atomic Mass

If elements contain isotopes with different masses, why does the periodic table usually show only one atomic mass for each element?

The value shown is generally a weighted average of the naturally occurring isotopes.

For example, naturally occurring chlorine is mainly a mixture of chlorine-35 and chlorine-37.

Its relative atomic mass is approximately:

35.45

This does not mean that a chlorine atom contains 35.45 nucleons.

Individual atoms have whole numbers of protons and neutrons.

The decimal value represents an average across a large number of naturally occurring chlorine atoms.

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A Simple Weighted-Average Example

Imagine an element exists as:

• 75% isotope-35
• 25% isotope-37

An approximate average mass would be:

Average mass = (0.75 × 35) + (0.25 × 37)

Calculate each contribution:

0.75 × 35 = 26.25

0.25 × 37 = 9.25

Therefore:

Average mass = 26.25 + 9.25

Average mass = 35.5

This explains why relative atomic masses on the periodic table are often decimals.

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Applications of Isotopes

Different isotopes have many scientific and technological applications.

Medicine

Radioactive isotopes can be used for:

• Medical imaging
• Diagnosis
• Cancer treatment

Archaeology

Carbon-14 can be used to estimate the age of once-living materials.

Industry

Radioisotopes can be used to:

• Monitor material thickness
• Detect leaks
• Trace the movement of substances

Scientific Research

Stable and radioactive isotopes can be used as tracers to follow substances through chemical, biological, and environmental systems.

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Isotopes, Ions, and Elements

These ideas are sometimes confused.

Different Isotope

Change the number of neutrons.

The element remains the same.

Different Ion

Change the number of electrons.

The element remains the same.

Different Element

Change the number of protons.

The identity of the element changes.

A useful summary is:

Change neutrons → different isotope

Change electrons → different ion

Change protons → different element

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Common Mistakes

Saying Isotopes Have Different Numbers of Protons

They do not.

Isotopes of the same element have the same number of protons.

Confusing Nucleon Number with Atomic Number

Remember:

Atomic number = protons

Nucleon number = protons + neutrons

Including Electrons in the Nucleon Number

Electrons are not nucleons.

Only protons and neutrons contribute to the nucleon number.

Assuming Isotopes Have Identical Masses

Different neutron numbers mean different nucleon numbers and therefore different masses.

Thinking a Decimal Relative Atomic Mass Is an Isotope

A value such as chlorine's approximately 35.45 is an average, not the nucleon number of an individual chlorine atom.

Confusing Isotopes with Ions

Isotopes differ in neutrons.

Ions differ in electrons.

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Check Your Understanding

1. Define an isotope.

2. What must be the same for two atoms to be isotopes of the same element?

3. What must be different?

4. Why do isotopes of the same element have different masses?

5. Carbon-13 has atomic number 6. How many protons and neutrons does it contain?

6. Determine the numbers of protons and neutrons in carbon-14.

7. Determine the numbers of protons and neutrons in ³⁷₁₇Cl.

8. An atom contains 12 protons and 13 neutrons. Identify the isotope and its nucleon number.

9. Explain why carbon-12 and carbon-14 are both carbon.

10. What is the difference between hydrogen-1, hydrogen-2, and hydrogen-3?

11. Why do isotopes generally have similar chemical properties?

12. Explain the difference between an isotope and an ion.

13. Why are relative atomic masses on the periodic table often decimals?

14. Uranium-235 and uranium-238 both contain 92 protons. Calculate the number of neutrons in each.

15. Explain why changing the number of protons produces a different element rather than a different isotope.

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Key Terms

• Isotope – an atom of an element with the same number of protons but a different number of neutrons.
• Proton – a positively charged particle in the nucleus.
• Neutron – an electrically neutral particle in the nucleus.
• Nucleon – a proton or neutron.
• Atomic number – the number of protons in a nucleus.
• Nucleon number – the total number of protons and neutrons.
• Isotope notation – a notation showing the element, nucleon number, and atomic number.
• Stable isotope – an isotope whose nucleus does not spontaneously undergo radioactive decay.
• Radioisotope – an isotope with an unstable, radioactive nucleus.
• Relative atomic mass – the weighted average mass of an element's naturally occurring isotopes.
• Isotopic abundance – the proportion of a particular isotope in a sample of an element.
• Tracer – an isotope used to follow the movement of a substance through a system.

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Key Takeaways

• Isotopes are atoms of the same element with the same number of protons but different numbers of neutrons.
• The number of protons determines the identity of an element.
• Different neutron numbers give isotopes different nucleon numbers and masses.
• Atomic number equals the number of protons.
• Nucleon number equals the number of protons plus neutrons.
• Use neutrons = nucleon number − atomic number to determine neutron number.
• Isotope notation identifies both the atomic number and nucleon number.
• Carbon-12, carbon-13, and carbon-14 are examples of isotopes of the same element.
• Hydrogen-1, hydrogen-2, and hydrogen-3 are also isotopes.
• Isotopes generally have very similar chemical properties because they have the same electron arrangement when neutral.
• Some isotopes are stable while others are radioactive.
• The relative atomic mass shown on the periodic table is usually a weighted average of naturally occurring isotopes.