Bohrs Model of Hydrogen Atom, Class 11 Chemistry Notes
Introduction
Bohr's model of the hydrogen atom, proposed by Niels Bohr in 1913, was a significant advancement in atomic theory. This model provided a quantum explanation for the hydrogen atom's structure, overcoming the limitations of Rutherford's atomic model, which could not explain the stability of atoms. Bohr's model successfully explained the spectral lines of hydrogen and laid the groundwork for modern quantum mechanics.
Key Postulates of Bohr's Model
1. Quantized Orbits:
- Electrons revolve around the nucleus in fixed, quantized orbits or energy levels, which are designated by quantum numbers (n = 1, 2, 3,...).
- The energy of an electron in a particular orbit is constant and does not change as long as it remains in that orbit.
2. Angular Momentum Quantization:
- The angular momentum of an electron in a given orbit is quantised and is an integral multiple of h/2π, where ( h) is Planck’s constant.
Mathematically, it is expressed as:
mvr = nh / 2π
where ( m ) is the mass of the electron, ( v ) is its velocity, ( r ) is the radius of the orbit, and ( n ) is the principal quantum number.
3. Energy Levels and Emission of Photons:
- When an electron jumps from a higher energy level (excited state) to a lower energy level (ground state), it emits energy in the form of a photon.
- The energy difference between the two levels corresponds to the energy of the emitted photon:
ΔE = E2−E1= hν
where ν is the frequency of the emitted radiation.
4. Stationary Orbits:
- Electrons in stationary orbits do not radiate energy. This postulate resolved the classical paradox where accelerating charged particles were expected to emit electromagnetic radiation, leading to the collapse of the atom.
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Bohr's Radius and Energy of Orbits
1. Bohr's Radius:
The radius of the nth orbit of the hydrogen atom is given by:
rn: n2h2ϵ0/ πme2
For the first orbit ( n = 1), this reduces to a value known as Bohr’s radius ( r_1 ≈0.529A˚
2. Energy of an Electron:
- The energy of an electron in the n^{th} orbit of a hydrogen atom is given by:
En = - 13.6eV /n2
This equation shows that energy is negative, indicating that the electron is bound to the nucleus.
Explanation of the Hydrogen Spectrum
Bohr's model explains the hydrogen emission spectrum, which consists of several spectral series:
Lyman Series: Transitions from higher energy levels to n = 1.
Balmer Series: Transitions from higher energy levels to n = 2.
Paschen Series: Transitions from higher energy levels to n = 3.
Each series corresponds to photons of different wavelengths, and these series are observed in different regions of the electromagnetic spectrum.
Limitations of Bohr's Model
While Bohr’s model was revolutionary, it had several limitations:
1. Multi-Electron Atoms:
Bohr’s model is primarily applicable to hydrogen and hydrogen-like (single-electron) atoms. It fails to accurately predict the spectra of multi-electron atoms.
2. Zeeman and Stark Effects:
The model does not explain the splitting of spectral lines in the presence of magnetic (Zeeman effect) or electric fields (Stark effect).
3. Wave-Particle Duality:
Bohr’s model does not account for the wave nature of electrons, as later described by de Broglie’s hypothesis and Schrödinger's wave equation.
4. No Explanation for the Fine Structure:
The fine structure of spectral lines, observed at higher resolutions, is not explained by Bohr’s model.
Conclusion:
Bohr’s model of the hydrogen atom was a pivotal development in atomic theory. It successfully explained the stability of the atom and the emission spectra of hydrogen, leading to a deeper understanding of atomic structure. Despite its limitations, Bohr’s model laid the foundation for the modern quantum mechanical model of the atom, which provides a more comprehensive understanding of atomic behavior.