The nucleus as a system of nucleons
An atom’s nucleus is a compact system made of two types of particles: protons and neutrons. Because both live in the nucleus, they are collectively called nucleons. The nucleus determines the atom’s nuclear identity and many nuclear properties (stability, radioactivity, reaction behavior), while the electrons mainly determine chemical behavior.
- Proton: carries +1 elementary charge; the number of protons sets the element.
- Neutron: electrically neutral; changing the number of neutrons changes the isotope and can strongly affect stability.
The three key counting numbers: Z, N, and A
Nuclear physics uses a compact set of integers to describe any nucleus:
- Atomic number, Z: number of protons in the nucleus.
- Neutron number, N: number of neutrons in the nucleus.
- Mass number, A: total number of nucleons (protons + neutrons).
They are related by a simple identity:
A = Z + NThis relationship is used constantly: if you know any two of the three, you can find the third.
Step-by-step conversions between Z, N, and A
Recipe 1: Find A from Z and N
- Listen to the audio with the screen off.
- Earn a certificate upon completion.
- Over 5000 courses for you to explore!
Download the app
- Start with
A = Z + N. - Add the proton count and neutron count.
Example: A nucleus has Z = 8 protons and N = 10 neutrons.
A = 8 + 10 = 18- The nucleus has 18 nucleons total.
Recipe 2: Find N from A and Z
- Rearrange:
N = A − Z. - Subtract the proton count from the mass number.
Example: Carbon-14 has A = 14 and Z = 6.
N = 14 − 6 = 8- Carbon-14 has 8 neutrons.
Recipe 3: Find Z from A and N
- Rearrange:
Z = A − N. - Subtract the neutron count from the mass number.
Example: A nucleus has A = 23 and N = 12.
Z = 23 − 12 = 11- Z = 11 corresponds to sodium (Na), so the nucleus is a sodium nuclide.
Nuclides and related terms (isotope, isobar, isotone)
Precise language matters in nuclear physics because changing Z or N changes the nucleus in different ways.
- Nuclide: a specific nucleus characterized by a particular pair (Z, N) (equivalently, Z and A). Example: a nucleus with Z = 6 and N = 8 is a specific nuclide (carbon-14).
- Isotopes: nuclides with the same Z (same element) but different N (different neutron count). Example: carbon-12 (Z=6, N=6) and carbon-14 (Z=6, N=8) are isotopes of carbon.
- Isobars: nuclides with the same A (same total nucleons) but different Z (and thus different elements). Example: carbon-14 (A=14, Z=6) and nitrogen-14 (A=14, Z=7) are isobars.
- Isotones: nuclides with the same N (same neutron count) but different Z. Example: carbon-14 (N=8, Z=6) and oxygen-16 (N=8, Z=8) are isotones.
| Category | What stays the same? | What changes? | Quick example pair |
|---|---|---|---|
| Isotopes | Z | N (and A) | ¹²C and ¹⁴C |
| Isobars | A | Z (and N) | ¹⁴C and ¹⁴N |
| Isotones | N | Z (and A) | ¹⁴C and ¹⁶O |
Standard nuclear notation
The standard compact symbol for a nuclide is:
^A_Z Xwhere:
Xis the chemical symbol (H, He, C, U, etc.).Z(subscript) is the atomic number (protons).A(superscript) is the mass number (protons + neutrons).
Because the element symbol X already implies Z (each element has a unique Z), you will also see simplified forms such as X-A (e.g., C-14) or just ^A X when Z is understood from X.
How to interpret a nuclide symbol (worked examples)
Example 1: Interpret ^{14}_{6}C
- Read Z from the subscript: Z = 6 (6 protons).
- Read A from the superscript: A = 14 (14 nucleons).
- Compute neutrons:
N = A − Z = 14 − 6 = 8. - Interpretation: carbon nucleus with 6 protons and 8 neutrons (carbon-14).
Example 2: Build the symbol from Z and N
A nucleus has Z = 17 and N = 18.
- Compute mass number:
A = Z + N = 17 + 18 = 35. - Element with Z = 17 is chlorine (Cl).
- Nuclide notation:
^{35}_{17}Cl(also written Cl-35).
Example 3: Identify whether two nuclei are isotopes, isobars, or isotones
Compare ^{40}_{20}Ca and ^{42}_{20}Ca.
- Z is the same (20 and 20) → same element.
- A differs (40 vs 42) → N differs.
- They are isotopes of calcium.
Compare ^{58}_{28}Ni and ^{58}_{26}Fe.
- A is the same (58) → same mass number.
- Z differs (28 vs 26) → different elements.
- They are isobars.
Compare ^{15}_{7}N and ^{16}_{8}O.
- Compute neutrons: for nitrogen-15,
N = 15 − 7 = 8; for oxygen-16,N = 16 − 8 = 8. - N is the same (8) → isotones.
Concept check: chemical behavior vs nuclear identity
1) What determines the element (chemical identity)?
Z determines the element. If Z changes, you have a different element. Chemical behavior is governed primarily by the electron structure, especially the number and arrangement of electrons. In a neutral atom, the number of electrons equals Z, so Z indirectly sets the electron count and thus chemistry.
2) What can change without changing the element?
N can change while Z stays the same. That produces different isotopes of the same element. Isotopes have nearly the same chemical behavior (because their electron structure is essentially the same for neutral atoms) but can have very different nuclear properties (stability, likelihood of radioactive decay, reaction thresholds).
3) Quick self-test items
- If two atoms have the same Z but different N, are they the same element? Are they the same nuclide?
- If Z changes from 11 to 12, what must happen to the element symbol? What happens to chemistry in a neutral atom?
- For
^{A}_{Z}X, which number(s) must you know to determine N? Which number alone determines the element?
