Atomic number, mass number and isotopes/isobars/isotones is a core Nuclei & Radioactivity concept in Physics. This guide explains what it is, walks through a fully worked example, and lists the key equations you need — with a short quiz to test yourself.

Key equations and worked example

Hydrogen (Z = 1) has one electron in the n = 1 shell. Bohr's model gives its energy levels Eₙ = −13.6/n² eV, so the ground state is −13.6 eV and the first excited state is −3.4 eV. Dropping from n = 2 to n = 1 emits a photon of 10.2 eV — the Lyman-alpha line. Helium (Z = 2) fills the first shell with 2 electrons; lithium (Z = 3) starts the second shell.

• <code>Bohr radius rₙ = n²·a₀ (a₀ ≈ 0.529 Å)</code>
• <code>Energy levels: Eₙ = −13.6·Z²/n² eV</code>
• <code>Photon emitted: ΔE = h·f = 13.6·Z²·(1/n₁² − 1/n₂²) eV</code>
• <code>Shell capacity: 2n² electrons</code>

Atomic number, mass number and isotopes/isobars/isotones in detail

Atomic number, mass number and isotopes/isobars/isotones is one of the central ideas in Nuclei &amp; Radioactivity, and it appears in Physics curricula under Nuclear structure. It is worth learning deeply because it connects to so many other topics in this section.

Bohr&#39;s model pictures electrons circling the nucleus in fixed shells of quantized angular momentum (mvr = n·h/2π), each shell holding at most 2n² electrons. It correctly predicts hydrogen&#39;s spectrum but is superseded by quantum mechanics, where &#39;orbits&#39; become probability clouds (orbitals). Still, shells explain the periodic table: elements in the same column have the same outer-shell electron count.

For exams, the pattern is predictable: first a definition or statement of the result, then a direct numerical application of one of the equations above, then a "why" question — why the formula takes that form, or what changes when a variable is doubled or halved. The worked example and quiz below cover exactly that progression.

Quick self-check:

• Q: How many electrons can the n = 2 shell hold?<br />A: 8 — capacity is 2n² = 2×4 = 8.
• Q: What photon is emitted when hydrogen&#39;s electron falls from n = 3 to n = 2?<br />A: ΔE = 13.6×(1/4 − 1/9) ≈ 1.89 eV — the red H-alpha line of the Balmer series.
• Q: Why don&#39;t orbiting electrons spiral into the nucleus in Bohr&#39;s model?<br />A: By postulate, electrons in allowed shells do not radiate; radiation happens only when jumping between shells.
• Q: Where does Bohr&#39;s model fail?<br />A: Multi-electron atoms, fine spectral structure, and the true probabilistic nature of orbitals — quantum mechanics replaces circular orbits with wavefunctions.