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2. Isotopes and decay page 6
Isotopes and stability
The nucleus of an atom contains protons and neutrons and it accounts for nearly all the mass of an atom. We can denote the number of nucleons in the nucleus using:
  • the atomic number: this is number of protons in the nucleus of an atom. It has the symbol Z. It is fixed for a given element.
  • the atomic mass number: this is the number of protons added to the number of neutrons and is given the symbol A.
Structure of nucleus A and Z graphic
Picture 2.1 Showing the atomic number and mass number of an atom. Notice that they come before the symbol. A is at the top and Z is at the bottom.
For example . . .
Nitrogen has the chemical symbol N.

It has an atomic number of 7 (Z=7) because it has 7 protons in its nucleus. We write this in front of the chemical symbol to the bottom-left.

Some nitrogen atoms have 15 nucleons in the nucleus and therefore have an atomic mass number of 15. Again, the atomic mass number, A, comes before the chemical symbol and is positioned top-left.

How does this tell us the number of neutrons?

A is the number of neutrons plus protons in the nucleus.
However, we already know that there are 7 protons.
Therefore, there must be 8 neutrons in the nucleus to add up to 15.

name symbol A Z neutrons
nitrogen-12 isotope 12 7 5
nitrogen-13 isotope 13 7 6
nitrogen-14 isotope 14 7 7
nitrogen-15 isotope 15 7 8
Table 3. Some of the isotopes of nitrogen. The atomic number is always 7. However, the atomic mass number, A, changes.
Number of neutrons
However, not all nitrogen nuclei have 8 neutrons in a nucleus. They can have 5, 6, 7, 8, 9, 10 or 11 neutrons. We call these different isotopes of nitrogen. There are always 7 protons because the nucleus is always a nitrogen nucleus (Z=7).

Since different isotopes of an element have different numbers of neutrons (but always the same number of protons) they have different mass numbers. The isotopes of nitrogen have mass numbers ranging from 12 to 18. We call them nitrogen-12, nitrogen-13, nitrogen-14 and so on.

Some isotopes of nitrogen are unstable. They give out radiation to become more stable; we say they are radioactive. Nitrogen-14 and nitrogen-15 are both stable isotopes of nitrogen. However, the other 5 isotopes are all unstable. Nitrogen-12 and nitrogen-13 will decay by beta plus emission and nitrogen-16, nitrogen-17 and nitrogen-18 decay by beta minus emission.

Stable isotopes
Every element has a number of different isotopes. Some of these are radioactive and some are stable. All the elements up to Z = 82 have at least one stable isotope.

We can plot a graph of stable isotopes. The atomic number, Z, is on the x-axis and the number of neutrons (N) is on the y-axis. The graph is a curve – see picture 2.2.

N Z plot of stable isotopes
Picture 2.2 Graph of stable isotopes.
For light elements (the bottom left of the graph), the stable isotopes are the ones with the same numbers of protons and neutrons and hence the ‘line of stability’ follows the straight line of N = Z. For example, the stable isotope carbon-12 has 6 protons and 6 neutrons.

If we got a straight line all the way, then this would tell us that the stable isotopes have the same number of neutrons as protons. However, this is not the case. The line curves upwards. Stable isotopes of the heavier elements (top right of the graph) have more neutrons than protons. For example, Gold-197 is stable. It contains 79 protons and 118 neutrons.

The neutrons in a nucleus can be thought of as acting as a kind of glue to hold the nucleus together. The positively charged protons are in a very confined space but would rather not be, due to the fact that they repel each other.

However, protons and neutrons are all attracted to each other as a result of another force - the strong nuclear force (see below). The neutrons don't contribute any repulsive effects because they are neutral. So having more neutrons around can help to hold the nucleus together. Notice that no amount of neutrons can hold a nucleus together once it has more that 82 protons – the line stops at Z = 82! All of the elements with an atomic number greater than 82 have only unstable isotopes.

Changing image to show strong nuclear force
Picture 2.3 Protons are held together by the strong nuclear force.
Forces in nucleus
We now know that the nucleus of helium is 1.9 x 10–15 m across. It contains two protons. They are both positively charged and will repel each other. However, they stay bound in a helium nucleus. Therefore there must be another force that holds them together.

This is the strong nuclear force. It is an attractive force that only has an effect over a very short range in nucleus (about 10–15 m - the size of the nucleus). The strong nuclear force binds protons and neutrons together to make the nucleus.

Neutrons and protons are made from quarks (see page 17).The strong nuclear force is actually a force between quarks and is carried by particles called gluons. Protons and neutrons are made of quarks and they feel the strong nuclear force as well. Electrons do not feel the strong nuclear force. Fundamental particles that don't feel the strong nuclear force are all in the family of leptons.

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Question 5
a) Carbon has an atomic number 6. How many neutrons are there in the nucleus of a carbon-15 atom?

b) What can you say about the ratio of the number of neutrons to the number of protons in stable:

i. light nuclei (atomic number less than 15)?

ii. heavy nuclei (atomic number about 80)?