understand that nucleon number and charge are conserved in nuclear processes

Atoms, Nuclei and Radiation

Learning Objective

Understand that the total nucleon number (mass number, \$A\$) and the total charge (atomic number, \$Z\$) are conserved in all nuclear processes.

Key Concepts

• Nucleon number (\$A\$): total number of protons and neutrons in a nucleus.
• Charge number (\$Z\$): number of protons, which determines the element.
• Conservation laws: In any nuclear reaction,

  \$A{\text{initial}} = A{\text{final}}, \qquad Z{\text{initial}} = Z{\text{final}}.\$

• Only the arrangement of nucleons may change; the total counts remain the same.

Common Nuclear Processes

1. Alpha (\$\alpha\$) Decay

An \$\alpha\$ particle is a \$^{4}_{2}\text{He}\$ nucleus (2 protons, 2 neutrons). The parent nucleus loses these nucleons.

General form:

\$^{A}{Z}\text{X} \;\rightarrow\; ^{A-4}{Z-2}\text{Y} \;+\; ^{4}_{2}\text{He}.\$

Both \$A\$ and \$Z\$ are reduced by the same amounts on both sides of the equation, preserving total values.

2. Beta Minus (\$\beta^{-}\$) Decay

A neutron transforms into a proton, emitting an electron and an antineutrino:

\$n \;\rightarrow\; p^{+} \;+\; e^{-} \;+\; \bar{\nu}_{e}.\$

For the nucleus:

\$^{A}{Z}\text{X} \;\rightarrow\; ^{A}{Z+1}\text{Y} \;+\; e^{-} \;+\; \bar{\nu}_{e}.\$

The mass number \$A\$ stays the same, while \$Z\$ increases by 1, keeping total charge conserved when the emitted electron is included.

3. Beta Plus (\$\beta^{+}\$) Decay (Positron Emission)

A proton converts into a neutron, emitting a positron and a neutrino:

\$p^{+} \;\rightarrow\; n \;+\; e^{+} \;+\; \nu_{e}.\$

For the nucleus:

\$^{A}{Z}\text{X} \;\rightarrow\; ^{A}{Z-1}\text{Y} \;+\; e^{+} \;+\; \nu_{e}.\$

Again \$A\$ is unchanged; \$Z\$ decreases by 1, balanced by the positive charge of the emitted positron.

4. Gamma (\$\gamma\$) Emission

Excited nuclei release excess energy as a photon:

\$^{A}{Z}\text{X}^{*} \;\rightarrow\; ^{A}{Z}\text{X} \;+\; \gamma.\$

No change in \$A\$ or \$Z\$; only energy is carried away.

Conservation Demonstrated with Example Reactions

Example 1: Alpha Decay of Uranium‑238

Reaction:

\$^{238}{92}\text{U} \;\rightarrow\; ^{234}{90}\text{Th} \;+\; ^{4}_{2}\text{He}.\$

Check conservation:

Example 2: Beta Minus Decay of Carbon‑14

Reaction:

\$^{14}{6}\text{C} \;\rightarrow\; ^{14}{7}\text{N} \;+\; e^{-} \;+\; \bar{\nu}_{e}.\$

Check conservation:

General Procedure for \cdot erifying Conservation

1. Write the nuclear equation, including all emitted particles.
2. Identify \$A\$ and \$Z\$ for each reactant and product.
3. Sum \$A\$ values on the left‑hand side (LHS) and right‑hand side (RHS); they must be equal.
4. Sum \$Z\$ values (including charges of emitted leptons); they must also be equal.
5. If the sums differ, the equation is not balanced and must be corrected.

Common Pitfalls

• For \$\beta^{-}\$ decay, forgetting to include the electron’s \$-1\$ charge when checking \$Z\$.
• For \$\beta^{+}\$ decay, forgetting the positron’s \$+1\$ charge.
• Assuming gamma emission changes \$A\$ or \$Z\$ – it does not.
• Neglecting neutrinos/antineutrinos in the balance of charge (they are neutral, so they do not affect \$Z\$).

Suggested Diagram

Summary

In every nuclear process, the total number of nucleons (\$A\$) and the total charge (\$Z\$) remain unchanged. By carefully accounting for all particles—including emitted leptons and photons—students can verify that these conservation laws hold, providing a solid foundation for further study of nuclear reactions and radiation.