Lewis Structures & Electron Distribution
Calculate formal charge to determine electron distribution in Lewis structures.
Number of electrons in outer shell of neutral atom
Lone pair electrons (usually even number)
Total bonds (single + double + triple)
Total electrons in bonds (must be even)
Formal charge is a bookkeeping tool to track electron distribution in Lewis structures. It helps identify the most stable resonance structures.
Best Structures: Minimize formal charges (aim for 0). Place negative charges on electronegative atoms. Avoid adjacent like charges.
The Bohr model, proposed by Niels Bohr in 1913, was a revolutionary quantum mechanical model of the hydrogen atom. It introduced the concept of quantized energy levels, explaining why atoms emit light at specific wavelengths rather than a continuous spectrum.
While the Bohr model has been superseded by more accurate quantum mechanical models (Schrödinger equation), it remains incredibly useful for understanding atomic structure and calculating the hydrogen spectrum. It successfully explains the Rydberg formula and predicts the correct wavelengths for hydrogen's spectral lines.
Energy of Level n:
En = -13.6 eV / n²
Energy of Transition:
ΔE = En₂ - En₁ = hf = hc/λ
Rydberg Equation:
1/λ = RH (1/n₁² - 1/n₂²)
The energy levels of hydrogen get closer together as n increases, asymptotically approaching zero energy (ionization) at n = ∞. The largest energy gap is between n = 1 and n = 2.
Energy increases (becomes less negative) as n increases. Ground state (n=1) is most stable.
When electrons transition between energy levels, they emit or absorb photons. Each series is named after its discoverer and corresponds to transitions ending at a particular n₁ level:
| Series | n₁ | n₂ Range | Region | λ Range |
|---|---|---|---|---|
| Lyman | 1 | 2, 3, 4, ... | Ultraviolet | 91-122 nm |
| Balmer | 2 | 3, 4, 5, ... | Visible | 365-656 nm |
| Paschen | 3 | 4, 5, 6, ... | Infrared | 820-1875 nm |
| Brackett | 4 | 5, 6, 7, ... | Infrared | 1.46-4.05 μm |
| Pfund | 5 | 6, 7, 8, ... | Infrared | 2.28-7.46 μm |
Balmer Series: The only series visible to the human eye! These transitions (n → 2) produce the characteristic red, blue-green, blue-violet, and violet lines of hydrogen's spectrum. The Hα line (n=3→2) at 656 nm is prominently red.
Problem:
Calculate the wavelength of light emitted when an electron in hydrogen transitions from n = 3 to n = 2 (the Balmer alpha or Hα line).
Step 1: Calculate energy of each level
E₂ = -13.6 eV / 2² = -13.6 / 4 = -3.40 eV
E₃ = -13.6 eV / 3² = -13.6 / 9 = -1.51 eV
Step 2: Calculate energy difference
ΔE = E₃ - E₂ = -1.51 - (-3.40) = 1.89 eV
Convert to Joules: 1.89 eV × 1.602×10⁻¹⁹ J/eV = 3.03×10⁻¹⁹ J
Step 3: Calculate wavelength using E = hc/λ
λ = hc / ΔE
λ = (6.626×10⁻³⁴ J·s)(2.998×10⁸ m/s) / (3.03×10⁻¹⁹ J)
λ = 6.56 × 10⁻⁷ m = 656 nm
Alternative: Use Rydberg equation
1/λ = RH (1/n₁² - 1/n₂²)
1/λ = 1.097×10⁷ (1/4 - 1/9) = 1.097×10⁷ (0.1389)
1/λ = 1.524×10⁶ m⁻¹
λ = 656 nm ✓
Answer:
The Hα line has a wavelength of 656 nm, which appears as red lightin the visible spectrum. This is one of the most prominent lines in hydrogen's emission spectrum and is used extensively in astronomy.
Hydrogen spectral lines (especially Hα) are used to study stars, nebulae, and galaxies. Redshift/blueshift of these lines reveals the velocity and distance of celestial objects.
Emission and absorption spectroscopy identify elements in unknown samples. Each element has a unique spectral fingerprint based on its electronic structure.
The Bohr model introduced quantization of energy, laying the groundwork for modern quantum mechanics. It demonstrated that classical physics fails at the atomic scale.
Understanding hydrogen spectra is crucial for fusion research and plasma diagnostics. The Balmer lines are monitored in fusion reactors to measure plasma conditions.
While successful for hydrogen, the Bohr model has significant limitations:
Only works for hydrogen-like ions
Cannot accurately predict spectra of multi-electron atoms
Doesn't explain fine structure
Cannot account for splitting of spectral lines in magnetic fields (Zeeman effect)
Violates Heisenberg uncertainty principle
Assumes precise knowledge of both position and momentum
No explanation for chemical bonding
Cannot predict molecular structures or bond formation
Modern Replacement: The Schrödinger equation and quantum mechanical orbital theory provide a more complete and accurate description of atomic structure, though the Bohr model remains pedagogically valuable.
1885: Johann Balmer
Empirically discovered the formula for hydrogen's visible spectral lines (Balmer series), not knowing the underlying physics.
1888: Johannes Rydberg
Generalized Balmer's formula to the Rydberg equation, covering all spectral series. Introduced the Rydberg constant.
1913: Niels Bohr
Developed quantum model explaining WHY the Rydberg equation works. Introduced quantized angular momentum and stationary states. Won 1922 Nobel Prize.
1926: Erwin Schrödinger
Formulated wave equation that completely describes atomic structure, superseding Bohr's model while confirming its main results for hydrogen.