distinguish between nucleon number and proton number

Atoms, Nuclei and Radiation

Distinguishing Nucleon Number and Proton Number

In nuclear physics two fundamental integer quantities are used to describe a nucleus:

• Proton number (also called atomic number) – the number of protons in the nucleus. It determines the chemical element and is denoted by $Z$.
• Nucleon number (also called mass number) – the total number of nucleons (protons + neutrons) in the nucleus. It is denoted by $A$.

The relationship between these quantities can be written as

$$A = Z + N$$ where $N$ is the neutron number. The three numbers $Z$, $N$, and $A$ uniquely identify a specific isotope of an element.

Key Differences

Aspect	Proton Number ($Z$)	Nucleon Number ($A$)
Definition	Count of protons in the nucleus	Count of all nucleons (protons + neutrons)
Symbol	$Z$	$A$
Determines	Chemical element (e.g., carbon, oxygen)	Isotope of the element (e.g., $^{12}$C vs $^{13}$C)
Typical Range	1 – 118 (known elements)	1 – \overline{300} for naturally occurring nuclei
Conservation in Reactions	Conserved in nuclear reactions that do not involve transmutation	Conserved in all nuclear reactions (mass number is conserved)

Practical Examples

1. For the nucleus of a carbon‑12 atom:
   • $Z = 6$ (six protons)
   • $A = 12$ (six protons + six neutrons)
2. For the nucleus of a uranium‑235 atom:
   • $Z = 92$ (ninety‑two protons)
   • $A = 235$ (ninety‑two protons + one hundred forty‑three neutrons)

Why the Distinction Matters

Understanding the difference between $Z$ and $A$ is essential for:

• Identifying isotopes and predicting their stability.
• Balancing nuclear equations, where both $Z$ and $A$ must be conserved.
• Interpreting decay modes (e.g., $\alpha$ decay reduces $A$ by 4 and $Z$ by 2).