Bohr Model and Line Spectra

Introduction to Bohr Model

• Scientists in the late 19th century aimed to understand light emitted from atoms and molecules, notably through line spectra.
• Line spectra are produced by exciting a gas at low partial pressure using electrical current or heating.

Emission Lines

• Each emission line consists of a single wavelength of light.
• This indicates that the light emitted by a gas only includes certain energies, not all.
• Key wavelengths involved (measured in Angstroms):
  • 4000 Å
  • 5000 Å
  • 6000 Å
  • 7000 Å

Historical Contributions

• Scientists Balmer and Rydberg developed equations to explain the observed line spectra.
• Niels Bohr extended these theories related to electrons in atoms, integrating concepts from Planck (quantization) and Einstein (photons).

Structure of the Atom

• The nucleus contains positively charged protons.
• Electrons placed at various distances from the nucleus possess energy:
  • The further an electron is from the nucleus, the more energy it possesses.
• Energy dependency is due to the work required to separate charges.

Energy Levels in the Bohr Model

• In a hydrogen atom, the electron can exist at various discrete energy levels denoted by n:
  • n = 1 (ground state)
  • n = 2 (first excited state)
  • n = 3 (second excited state)

Energy Absorption and Emission

• Electrons can move to a higher energy level by absorbing energy in the form of a photon.

- Conversely, when they return to a lower energy level, they release energy as a photon.

Formula for Energy Levels

• The energy of an electron at a specific level is given by the equation: E_n = -2.18 \times 10^{-18} \text{ J} \left( \frac{1}{n^2} \right)
  • Where n is the principal quantum number (energy level).

Energy Change During Transitions

• The change in energy when an electron transitions between two energy levels is described by: \Delta E = 2.18 \times 10^{-18} \text{ J} \left( \frac{1}{ni^2} - \frac{1}{nf^2} \right)
  • This can also be expressed in an equivalent, simpler form:
    \Delta E = -2.18 \times 10^{-18} \text{ J} \left( \frac{1}{nf^2} - \frac{1}{ni^2} \right)
  • Where ni is the initial energy level and nf is the final energy level.

Conclusion

• The Bohr model provides a foundational understanding of atomic structure and electron behavior, leading to significant advancements in quantum mechanics.