Nuclides, Isotopes, and Nuclear Notation

A nuclide is a nuclear species specified by proton number, neutron number, and nuclear energy state. Precise notation matters because radiation properties belong to nuclides, not merely to element names.

Learning objectives

You will interpret nuclide notation, calculate proton and neutron counts, distinguish isotopes, isobars, and isotones, identify metastable states and ions, and conserve nuclear bookkeeping in transformations.

Standard notation

Write

$${}^{A}_{Z}\mathrm{X},$$

where $Z$ is proton number, $N$ neutron number, and

$$A=Z+N.$$

The element symbol already determines $Z$, so compact forms such as carbon-14 or $\mathrm{^{14}C}$ are common. The left superscript is a count, not a measured mass in unified atomic mass units. Mass number $A$ is always an integer; the nuclide’s actual atomic mass is not.

To read a symbol reliably, use a fixed sequence: identify $Z$ from the subscript or element symbol, identify $A$ from the superscript, then compute $N=A-Z$. Treat charge and metastable labels as separate information.

Relationships among nuclides

• Isotopes: same $Z$, different $N$.
• Isobars: same $A$, different $Z$.
• Isotones: same $N$, different $Z$.
• Nuclear isomers: same $Z$ and $A$, different nuclear energy states.

A metastable isomer may be written with $m$, as in $\mathrm{^{99m}Tc}$. This $m$ describes nuclear excitation, not mass or an ionic charge.

Nuclear equations

In a nuclear transformation, total mass number and charge number balance. For a generic alpha decay,

$${}^{A}_{Z}\mathrm{X} \longrightarrow {}^{A-4}_{Z-2}\mathrm{Y} +{}^{4}_{2}\mathrm{He}.$$

This conservation bookkeeping constrains possible daughters but does not by itself determine whether a decay is energetically allowed.

Balance equations by counting nucleons and charge number on both sides. Do not balance element symbols as though the expression were a chemical equation. Neutrinos and photons have $A=0$ and $Z=0$, yet they can be essential for energy, momentum, and angular-momentum conservation.

Identity versus amount

Nuclide notation identifies a nuclear species; it does not state how much material is present or how rapidly it transforms. Mass, number of atoms, activity, and half-life are different quantities. A complete source record may therefore need the nuclide, activity, reference date and time, chemical form, and physical form.

Common mistakes

• Subtracting in the wrong direction when finding $N=A-Z$.
• Calling two equal-$A$ nuclides isotopes; they are isobars unless they also share $Z$.
• Treating an ionic charge as part of the mass number.
• Omitting the metastable label when it distinguishes a different nuclear state.

Test Your Knowledge

1. Find $Z$ and $N$ for $\mathrm{^{137}_{55}Cs}$.
2. Classify $\mathrm{^{14}C}$ and $\mathrm{^{12}C}$.
3. What does the $m$ mean in $\mathrm{^{99m}Tc}$?
4. Are $\mathrm{^{40}_{18}Ar}$ and $\mathrm{^{40}_{20}Ca}$ isotopes, isotones, or isobars?
5. Complete the daughter indices for $\mathrm{^{210}_{84}Po}$ alpha decay.

Solutions

1. $Z=55$ and $N=82$.
2. They are isotopes.
3. A metastable excited nuclear state.
4. Isobars: they share $A=40$ but have different $Z$.
5. $A=210-4=206$ and $Z=84-2=82$, so the daughter is $\mathrm{^{206}_{82}Pb}$.

Connection forward

Nuclear stability asks why some combinations of $Z$ and $N$ persist while others transform spontaneously.

Sources

• IAEA LiveChart of Nuclides for evaluated nuclide identities and properties.
• NIST Atomic Weights and Isotopic Compositions for isotopic-composition and relative-mass reference data.