Bohr Model Calculator
Calculate electron transitions, energy levels, and orbital properties for hydrogen-like atoms
Calculate Bohr Model Properties
Principal quantum number (1, 2, 3, ...)
Target quantum number
1=H, 2=He⁺, 3=Li²⁺, etc.
Initial Energy
Final Energy
Photon Frequency
Wavelength
Electromagnetic Spectrum
Spectrum Region: Visible light - Human eye detection
Hydrogen Series: Balmer series (Visible)
Transition: n=3 → n=2
Process: Electron jumps to higher energy
Bohr Model Formulas
Energy Levels: E_n = -13.6057 × Z² / n² eV
Energy Difference: ΔE = E₂ - E₁ = hf
Photon Frequency: f = |ΔE| / h
Wavelength: λ = c / f
Example Calculation
Hydrogen Balmer Series (n=3 → n=2)
Initial State: n₁ = 3 (first excited state)
Final State: n₂ = 2 (second energy level)
Atom: Hydrogen (Z = 1)
Transition: Visible light emission (red line at 656 nm)
Bohr Model Calculation
1. Calculate initial energy: E₃ = -13.6 × 1² / 3² = -1.51 eV
2. Calculate final energy: E₂ = -13.6 × 1² / 2² = -3.40 eV
3. Energy difference: ΔE = -3.40 - (-1.51) = -1.89 eV
4. Photon frequency: f = 1.89 eV / 4.136×10⁻¹⁵ eV·s = 457 THz
5. Wavelength: λ = c / f = 656 nm (red visible light)
Result: Emission of red photon in Balmer series
Hydrogen Energy Levels
Hydrogen Spectral Series
Lyman (n→1)
Ultraviolet
Balmer (n→2)
Visible light
Paschen (n→3)
Near infrared
Brackett (n→4)
Mid infrared
Bohr Model Principles
Quantized Orbits: Electrons in discrete energy levels
Angular Momentum: L = nℏ (quantized)
Photon Emission: Energy difference = hf
Stationary States: No radiation in orbits
Understanding the Bohr Model
What is the Bohr Model?
The Bohr model, proposed by Niels Bohr in 1913, describes the hydrogen atom as an electron orbiting a nucleus in quantized energy levels. This revolutionary model explained the discrete spectral lines of hydrogen and introduced quantum mechanics concepts.
Key Principles
- •Quantized Orbits: Electrons occupy discrete energy levels
- •Stationary States: No energy radiated in stable orbits
- •Photon Transitions: Energy absorbed/emitted during level changes
Applications
The Bohr model successfully explains hydrogen spectra, provides foundation for quantum mechanics, and helps understand atomic structure and chemical bonding principles.
Modern Applications
- •Spectroscopy: Analysis of atomic and molecular spectra
- •Astronomy: Understanding stellar composition and temperatures
- •Lasers: Population inversion and stimulated emission
- •Quantum Electronics: Foundation for modern devices
Mathematical Framework
E_n = -13.6057 Z² / n² eV
Energy levels formula
r_n = n² a₀ / Z
Orbital radius formula
f = |E₂ - E₁| / h
Photon frequency
v_n = α c Z / n
Orbital velocity
• Rydberg energy: 13.6 eV
• Bohr radius: 0.529 Å
• Fine structure: α = 1/137
• Principal: n = 1, 2, 3, ...
• Energy: E ∝ -1/n²
• Radius: r ∝ n²
• Only hydrogen-like atoms
• Classical orbit concept
• Superseded by quantum mechanics