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Part of PH-02 — Atoms & Nuclei

Overview (~400 words): SVG Diagram + Tables

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Visual Overview: Atoms & Nuclei

Hydrogen Energy Level Diagram:

H Energy Levels and Spectral Regions n=1 -13.6 eV n=2 -3.4 eV n=3 -1.51 eV n=4 -0.85 eV n=5 -0.54 eV n=∞ 0 eV Lyman (UV) Balmer (Vis) Paschen (IR)

Bohr Model Quick Reference:

Quantity	Formula	n=1,Z=1 (Ground H)	n=2,Z=1	n=3,Z=1
Radius	0.529 $n^{2}$ /Z Å	0.529 Å	2.116 Å	4.761 Å
Velocity	$2.18 \times 10^{6}$ Z/n m/s	$2.18 \times 10^{6}$ m/s	$1.09 \times 10^{6}$ m/s	$0.727 \times 10^{6}$ m/s
Energy	−13.6 $Z^{2}$ / $n^{2}$ eV	−13.6 eV	−3.4 eV	−1.511 eV
KE	+13.6 $Z^{2}$ / $n^{2}$ eV	+13.6 eV	+3.4 eV	+1.511 eV
PE	−27.2 $Z^{2}$ / $n^{2}$ eV	−27.2 eV	−6.8 eV	−3.022 eV

Nuclear Properties Table:

Property	Formula	Value/Notes
Nuclear radius	R = 1.2 × A^(1/3) fm	~1.2–8 fm depending on A
Nuclear density	ρ = Am_u/V	≈ $2.3 \times 10^{17}$ kg/ $m^{3}$ (constant)
Mass defect	$\Delta m$ = [Zm_p+(A-Z)m_n]−M	Always positive for stable nuclei
Binding energy	BE = $\Delta m$ × 931.5 MeV	Ranges from ~7 to ~8.75 MeV/nucleon
Most stable	Fe-56	BE/A ≈ 8.75 MeV/nucleon
Half-life	t_{1}/_{2} = 0.693/λ	Property of each isotope
Mean life	τ = 1/λ = 1.443 t_{1}/_{2}	Always > t_{1}/_{2}

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