Stable and Unstable Isotopes Explained for HSC Chemistry
Learn how isotopes can be atoms of the same element but have different neutron numbers, and why some nuclei are stable while others undergo radioactive decay.
A carbon atom in the graphite of your pencil and a radioactive carbon atom can have the same number of protons and behave almost identically in ordinary chemical reactions. Yet one nucleus can remain unchanged indefinitely, while the other eventually transforms into something else.
How can two atoms of the same element have such different nuclear behaviour?
Start with a prediction. Carbon is defined by having 6 protons. Suppose one carbon atom has 6 neutrons and another has 8 neutrons. Are they still the same element?
Yes. The number of protons decides the element. Changing the number of neutrons changes the isotope, not the element.
That distinction is the key to understanding stable and unstable isotopes.
01Isotopes change the nucleus without changing the element
Picture the nucleus as a tiny cluster of protons and neutrons.
For carbon:
- every carbon nucleus contains 6 protons
- one carbon nucleus might contain 6 neutrons
- another might contain 7 neutrons
- another might contain 8 neutrons
These are all carbon because their proton number is still 6.
They are different isotopes of carbon because their neutron numbers are different.
So the useful definition is:
Isotopes are atoms of the same element with the same number of protons but different numbers of neutrons.
That means isotopes have the same atomic number, but different mass numbers.
The atomic number, \(Z\), is the number of protons.
The mass number, \(A\), is the total number of protons and neutrons:
\[
A = Z + N
\]
where \(N\) is the number of neutrons.
Rearranging:
\[
N = A – Z
\]
Check your understanding
Two atoms contain:
- Atom X: 17 protons and 18 neutrons
- Atom Y: 17 protons and 20 neutrons
Are they isotopes of the same element?
Answer: Yes.
Both atoms have 17 protons, so both are chlorine atoms. Their neutron numbers are different, so they are different chlorine isotopes.
Their mass numbers are:
\[
A_X = 17 + 18 = 35
\]
\[
A_Y = 17 + 20 = 37
\]
So they are chlorine-35 and chlorine-37.
02Reading isotope notation
An isotope can be written using nuclide notation:
\[
\ce{^{A}_{Z}X}
\]
Here:
- \(X\) is the chemical symbol
- \(Z\) is the atomic number, or number of protons
- \(A\) is the mass number, or protons plus neutrons
For example:
\[
\ce{^{14}_{6}C}
\]
This carbon nucleus contains:
- 6 protons
- \(14 – 6 = 8\) neutrons
It is called carbon-14.
Compare it with:
\[
\ce{^{12}_{6}C}
\]
Carbon-12 still has 6 protons, but it has:
\[
12 – 6 = 6
\]
neutrons.
Same element. Different isotope.
Worked example: Are these atoms isotopes?
Consider \(\ce{^{24}_{12}Mg}\) and \(\ce{^{26}_{12}Mg}\). Explain whether they are isotopes and determine the number of neutrons in each nucleus.
Step 1Compare the proton numbers
Both nuclei have atomic number \(Z = 12\).
That means both contain 12 protons and are therefore magnesium.
Step 2Calculate the neutron number of magnesium-24
\[
N = A – Z = 24 – 12 = 12
\]
Magnesium-24 contains 12 neutrons.
Step 3Calculate the neutron number of magnesium-26
\[
N = A – Z = 26 – 12 = 14
\]
Magnesium-26 contains 14 neutrons.
Step 4Interpret the result
The atoms have the same proton number but different neutron numbers, so they are isotopes of magnesium.
03Why some nuclei are stable and others are not
So far, adding or removing neutrons sounds almost harmless. It isn’t.
Inside a nucleus, two important effects are competing.
Protons repel other protons because they all have positive electric charge. At the same time, the strong nuclear force attracts nearby protons and neutrons and helps hold the nucleus together.
A useful first picture is a crowded group trying to stay together.
The strong nuclear force is like everyone linking arms. The electrical repulsion between protons is like some members of the group pushing each other apart. Neutrons contribute to the attractive nuclear interaction without adding another positive charge.
That picture helps explain why neutrons can contribute to nuclear stability.
But it has an important limitation: you cannot simply keep adding neutrons and make a nucleus more stable forever. A nucleus needs an appropriate balance of protons and neutrons.
04Stable isotopes
A stable isotope has a nucleus that does not spontaneously undergo radioactive decay.
For example, both carbon-12 and carbon-13 are stable:
| Isotope | Protons | Neutrons | Nuclear behaviour |
|---|---|---|---|
| \(\ce{^{12}_{6}C}\) | 6 | 6 | Stable |
| \(\ce{^{13}_{6}C}\) | 6 | 7 | Stable |
| \(\ce{^{14}_{6}C}\) | 6 | 8 | Unstable |
Notice what this table tells us.
Having more neutrons does not automatically make an isotope unstable. Carbon-13 has one more neutron than carbon-12 and is still stable.
But carbon-14 has a neutron-proton combination that is unstable.
“Stable” also doesn’t mean that a nucleus could never be changed under any imaginable conditions. It means it does not spontaneously undergo radioactive decay under ordinary conditions.
05Unstable isotopes
An unstable isotope has a nucleus that can spontaneously change into a more stable nuclear arrangement.
This process is called radioactive decay.
An unstable isotope is therefore also called a radioisotope or radioactive isotope.
During radioactive decay, the nucleus releases radiation. Depending on the isotope and the decay process, this may involve particles, electromagnetic radiation, or both.
The important idea here is not yet the exact type of radiation. It is the reason decay occurs:
An unstable nucleus has a nuclear arrangement that can change spontaneously into a lower-energy, more stable arrangement.
Radioactive decay changes the nucleus, so it is fundamentally different from an ordinary chemical reaction, which mainly involves electrons.
Prediction question
Carbon-12 and carbon-14 are both neutral carbon atoms. Would you expect them to have completely different electron arrangements?
Answer: No.
Both have 6 protons. A neutral atom therefore has 6 electrons, so both have the same basic electron configuration.
Their main difference is inside the nucleus.
This is why isotopes of the same element usually have very similar chemical properties, even though their nuclear stability can be very different.
06Why the neutron-proton balance matters
For small stable nuclei, the number of neutrons is often similar to the number of protons.
For example:
\[
\ce{^{12}_{6}C}
\]
has 6 protons and 6 neutrons.
As nuclei become larger, the situation changes. More protons means more electrical repulsion inside the nucleus, so heavier stable nuclei generally require proportionally more neutrons.
This means there is no single rule such as:
“A stable nucleus must have equal numbers of protons and neutrons.”
That works reasonably well as an early pattern for some small nuclei, but it is not a general law.
Nuclear stability depends on the overall arrangement and balance of nucleons, where nucleons means protons and neutrons.
You will often see stable nuclei described as lying within a band of stability when neutron number is plotted against proton number.
The exact pattern is more complicated than a simple ratio, but for HSC Chemistry the central idea is clear:
- too few neutrons can produce an unstable nucleus
- too many neutrons can also produce an unstable nucleus
- the appropriate neutron-proton balance depends on the size of the nucleus
Check your understanding
A student says, “Neutrons stabilise nuclei, so an isotope with more neutrons must always be more stable.”
What is wrong with this reasoning?
Answer: Neutrons can contribute to nuclear stability because they participate in the strong nuclear interaction without adding proton-proton electrical repulsion. However, stability depends on the overall neutron-proton balance.
Adding neutrons indefinitely does not keep increasing stability. An excess of neutrons can also produce an unstable nucleus.
07Worked example: Hydrogen shows why neutron number matters
Hydrogen gives us a particularly clean comparison.
Consider these three isotopes:
\[
\ce{^{1}_{1}H}, \qquad \ce{^{2}_{1}H}, \qquad \ce{^{3}_{1}H}
\]
Explain what makes them isotopes and compare their nuclear stability.
Step 1Identify the proton number
Each isotope has atomic number \(Z = 1\).
Each therefore contains one proton, so all three are hydrogen.
Step 2Calculate the neutron numbers
For hydrogen-1:
\[
N = 1 – 1 = 0
\]
For hydrogen-2:
\[
N = 2 – 1 = 1
\]
For hydrogen-3:
\[
N = 3 – 1 = 2
\]
Step 3Compare their stability
Hydrogen-1 and hydrogen-2 are stable.
Hydrogen-3, also called tritium, is radioactive.
Step 4Interpret the result
All three nuclei contain the same number of protons, so they are the same element. Their different neutron numbers make them different isotopes.
The example also shows that simply adding another neutron can change nuclear stability. Hydrogen-2 is stable, while hydrogen-3 is unstable.
08Worked example: Carbon-14 behaves like carbon chemically, but not nuclearly
Suppose an organism contains both carbon-12 and carbon-14 atoms.
A student argues:
“Carbon-14 is radioactive, so it should behave like a completely different element.”
Explain the mistake.
Step 1Compare the proton numbers
Both carbon-12 and carbon-14 contain 6 protons.
The proton number determines the element, so both are carbon.
Step 2Compare the electron structures
A neutral atom of either isotope contains 6 electrons.
Their electron structures are therefore essentially the same.
Step 3Identify where the important difference occurs
Carbon-12 contains:
\[
12 – 6 = 6
\]
neutrons.
Carbon-14 contains:
\[
14 – 6 = 8
\]
neutrons.
The important difference is in the nucleus.
Step 4Interpret the result
Carbon-14 can participate in carbon-containing compounds because it is still carbon. However, its nucleus is unstable and undergoes radioactive decay.
That combination is exactly why radioactive isotopes can be useful as tracers and dating tools. Chemically, they can follow the behaviour of the element. Nuclearly, their radiation or decay can be detected.
09The misconception that causes the most trouble
Students sometimes think:
Different mass number = different element.
That is backwards.
When identifying an element, look at the proton number first.
| What changes? | What does it mean? |
|---|---|
| Number of protons | Different element |
| Number of neutrons only | Different isotope of the same element |
| Number of electrons only | Different ion or charge state |
| Nuclear stability | Determines whether the isotope is stable or radioactive |
For example:
- \(\ce{^{12}_{6}C}\) and \(\ce{^{14}_{6}C}\) are isotopes because both have 6 protons.
- \(\ce{^{14}_{6}C}\) and \(\ce{^{14}_{7}N}\) are not isotopes of each other. They have the same mass number, but different proton numbers, so they are different elements.
Quick check
Are \(\ce{^{35}_{17}Cl}\) and \(\ce{^{37}_{17}Cl}\) isotopes?
Answer: Yes. Both contain 17 protons but different numbers of neutrons.
Are \(\ce{^{40}_{18}Ar}\) and \(\ce{^{40}_{20}Ca}\) isotopes?
Answer: No. They have the same mass number, but different proton numbers. One is argon and the other is calcium.
10What this lets you understand next
Once you separate element identity from nuclear stability, radioactive chemistry becomes much easier.
The next useful question is no longer “What is an isotope?” It is:
What does an unstable nucleus actually do when it decays?
That leads directly into alpha decay, beta decay, gamma radiation, nuclear equations, and half-life.