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Formulas

Energy Levels in Bohr Model

Energy of electron in nth orbit of hydrogen atom.

Physics
Subject
Quantum Mechanics
Sub Subject
Atomic Structure
Chapter
Bohr Model
Topic

Energy Levels in Bohr Model

📊 intermediate
$$E_n = -\frac{m e^4}{8 \epsilon_0^2 h^2 n^2} = -\frac{13.6\,\text{eV}}{n^2}$$
Energy of electron in nth orbit of hydrogen atom.
Variables & Units
$E_n$
Energy of orbit
Unit: $\text{J}$ or $\text{eV}$
$n$
Principal quantum number
Unit: $\text{unitless}$
$m$
Electron mass
Unit: $\text{kg}$
$e$
Elementary charge
Unit: $\text{C}$
$\epsilon_0$
Vacuum permittivity
Unit: $\text{F/m}$
$h$
Planck's constant
Unit: $\text{J·s}$
Key Information
📐 Derived From
$E = K + U = -ke^2/(2r)$ and $r_n = n^2 a_0$
💡 Example
$n=2$: $E_2 = -13.6/4 = -3.4\,\text{eV}$.
🔧 Applications
Atomic spectroscopy, laser physics, astrophysics
⚠️ Constraints
Hydrogen atom, non-relativistic

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