KAHIBARO
Table of Contents
Distinguishing by Neutron Number
In nuclear physics, isotones are nuclei that have the same number of neutrons, but different numbers of protons. The neutron number is usually written as $N$, while the proton number, or atomic number, is written as $Z$.
If two nuclei are isotones, then they share the same $N$ value, even though they are different chemical elements because their $Z$ values are different.
For example, consider
$$
{}^{14}_{6}\mathrm{C}
\quad \text{and} \quad
{}^{15}_{7}\mathrm{N}
$$
For carbon, the neutron number is
$$
N = A - Z = 14 - 6 = 8
$$
For nitrogen, the neutron number is
$$
N = A - Z = 15 - 7 = 8
$$
So these two nuclei are isotones because both contain 8 neutrons.
Two nuclei are isotones if and only if they have the same neutron number $N$ and different proton numbers $Z$.
How to Identify Isotones
To check whether nuclei are isotones, use the relation
$$
N = A - Z
$$
where $A$ is the mass number and $Z$ is the atomic number.
After finding $N$ for each nucleus, compare the values. If the neutron numbers match, the nuclei are isotones.
Important formula:
$$
N = A - Z
$$
This is the key relation for identifying isotones.
Examples
The following table shows some isotone pairs.
| Nucleus | $A$ | $Z$ | $N = A-Z$ |
|---|---|---|---|
| ${}^{13}_{6}\mathrm{C}$ | 13 | 6 | 7 |
| ${}^{14}_{7}\mathrm{N}$ | 14 | 7 | 7 |
| ${}^{15}_{8}\mathrm{O}$ | 15 | 8 | 7 |
These three nuclei are all isotones because each has 7 neutrons.
Another example:
| Nucleus | $A$ | $Z$ | $N = A-Z$ |
|---|---|---|---|
| ${}^{39}_{19}\mathrm{K}$ | 39 | 19 | 20 |
| ${}^{40}_{20}\mathrm{Ca}$ | 40 | 20 | 20 |
| ${}^{41}_{21}\mathrm{Sc}$ | 41 | 21 | 20 |
All of these are isotones with $N=20$.
Comparison with Similar Terms
It is easy to confuse isotones with similar nuclear terms. The difference is based on which number stays the same.
| Term | Same quantity | Different quantity |
|---|---|---|
| Isotopes | Proton number $Z$ | Neutron number $N$ |
| Isobars | Mass number $A$ | Proton number $Z$, neutron number $N$ |
| Isotones | Neutron number $N$ | Proton number $Z$ |
So isotones are grouped by equal neutron count.
Why Isotones Matter
The neutron number strongly affects nuclear stability and nuclear structure. Because isotones all have the same number of neutrons, comparing them helps physicists study how changing the proton number changes the nucleus while keeping the neutron count fixed.
This is useful when looking for patterns in nuclear behavior, such as changes in stability, binding, and shell effects.
Visualizing Isotones
A simple way to picture isotones is to imagine moving across different elements while keeping the neutron count unchanged.
All points on the same horizontal line have the same neutron number, so they are isotones.
A Quick Check
Suppose we compare
$$
{}^{16}_{8}\mathrm{O}, \quad {}^{17}_{9}\mathrm{F}, \quad {}^{18}_{10}\mathrm{Ne}
$$
Their neutron numbers are
$$
16-8=8, \quad 17-9=8, \quad 18-10=8
$$
So all three are isotones.
When checking isotones, do not compare the mass number $A$ directly. Always calculate the neutron number using $N = A - Z$.
Summary
Isotones are nuclei with the same number of neutrons and different numbers of protons. They are identified using
$$
N = A - Z
$$
This idea helps organize nuclei and compare how nuclear properties change when neutron number is held constant.