Introduction to Bohr’s Model

• Proposed by Niels Bohr in 1913 to explain the structure of the hydrogen atom.
• Combined concepts of classical physics and quantum theory.

Postulates of Bohr’s Model

• Stationary Orbits
  • Electrons revolve around the nucleus in specific circular orbits called stationary orbits.
  • Each orbit corresponds to a fixed energy level, so electrons do not radiate energy while in these orbits.

• Quantization of Angular Momentum
  • The angular momentum of an electron in orbit is quantized: L=nℏ=nh/2π, where n is the principal quantum number, ℏ is the reduced Planck’s constant.

• Energy Levels
  • Electrons can move between orbits by absorbing or emitting energy: ΔE=E₂−E₁=hν
    • h= Planck’s constant, ν = frequency of emitted/absorbed radiation.
• Radiation of Energy
  • When an electron jumps from a higher energy orbit (n₂) to a lower energy orbit (n₁), it emits energy as photons.

Key Features of Bohr’s Model

• Energy Levels
  • The energy of the electron is inversely proportional to the square of the orbit number (n): Eₙ=(−13.6/n²)eV
    • Negative sign indicates the electron is bound to the nucleus.
• Radius of Orbits
  • The radius of the nth orbit is proportional to rₙ=n²×r₁
    • r₁=0.53 A˚(Bohr radius).

• Hydrogen Spectrum
  • Explained the emission spectrum of hydrogen (Lyman, Balmer, Paschen, etc.).

Achievements of Bohr’s Model

1. Successfully explained the spectral lines of hydrogen.
2. Introduced the concept of quantized energy levels.
3. Laid the foundation for modern atomic physics.

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Limitations of Bohr’s Model

• Applicable Only to Hydrogen-like Atoms
  • Could not explain spectra of atoms with more than one electron (e.g., Helium, Lithium).
• No Explanation for Spectral Line Splitting
  • Could not explain the fine structure (splitting of spectral lines in magnetic/electric fields) observed in the Zeeman and Stark effects.
• Fails to Address Wave-Particle Duality
  • Does not consider the wave-like nature of electrons (proposed later by de Broglie).
• Violation of Uncertainty Principle
  • Assumes precise paths (orbits) for electrons, contradicting Heisenberg’s Uncertainty Principle.
• No Explanation for Chemical Bonding
  • Fails to account for the behavior of electrons in chemical bonding.

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Bohr’s Model and Modern Atomic Theory

• Bohr’s model was replaced by the Quantum Mechanical Model of the Atom, which incorporates wave-particle duality and probability distributions of electrons.

Conclusion

• Bohr’s model was a significant step in understanding atomic structure and paved the way for further advancements in quantum mechanics.

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