The Bohr model of the hydrogen atom was the first atomic model to successfully explain the atomic hydrogen radiation spectra. Niels Bohr proposed the atomic hydrogen model in 1913. The Bohr model of the hydrogen atom attempts to fill in some of the gaps left by Rutherford's model. It has a special place in history because it introduced the quantum theory, which gave rise to quantum mechanics.
In comparison to the valence shell atom model, the Bohr model is a more rudimentary representation of the hydrogen atom. It may be determined as a first-order approximation of the hydrogen atom using the broader and far more precise quantum mechanics and hence may be regarded as an obsolete scientific theory.
Postulates
Bohr proposed the following fundamental postulates to explain the stability of the atom and the hydrogen line spectrum:
Electrons Revolve in Fixed Orbits
- Electrons revolve around the nucleus only in certain permitted circular paths called stationary orbits or energy levels (K, L, M, N).
- While moving in these orbits, electrons do not radiate energy.
Quantization of Angular Momentum
The angular momentum of an electron is quantized:
mvr = \frac{nh}{2\pi}
Where:
- mmm = mass of electron
- v = velocity
- r = radius of orbit
- n=1,2,3,… (principal quantum number)
- h = Planck’s constant
Fixed Energy of Each Orbit
- Each orbit has a definite energy.
Energy of electron in nth orbit is:
E_n = -\frac{13.6}{n^2} \text{ eV}
- The negative sign shows the electron is bound to the nucleus.
Emission or Absorption of Energy
- An electron emits or absorbs energy only when it jumps from one orbit to another.
E = h\nu
Where:
- h = Planck’s constant
- ν = frequency of radiation
Planetary Model of the Atom
- The planetary model of the atom compares the structure of an atom to the solar system.
- In this model, electrons revolve around a central nucleus like planets revolve around the sun.
- The atom has a very small, dense, positively charged nucleus at the center.
- Almost all the mass of the atom is concentrated in the nucleus.
- Electrons revolve around the nucleus in circular paths.
- Most of the space inside the atom is empty.
Limitations
- According to classical physics, revolving electrons should lose energy.
- Electrons should fall into the nucleus.
- It could not explain the hydrogen line spectrum.
Bohr’s Equation
- The Bohr model of the hydrogen atom was proposed by Niels Bohr in 1913.
- It was based on the planetary model suggested earlier by Ernest Rutherford, but Bohr introduced an important new assumption—that the energy of electrons in an atom is quantized.
- Bohr proposed that electrons revolve around the nucleus in fixed circular orbits called energy levels or shells.
- These orbits have specific radii, and electrons cannot exist between them
r_n = n^2 r_1
where:
- n = principal quantum number (1, 2, 3, …)
- r1 = radius of the first orbit (Bohr’s radius)
r(1) = 0.529 × 10-10 m
By considering electrons in circular, quantized orbits, Bohr calculated the energy of an electron in the nth level of hydrogen as:
E_n = -\frac{13.6}{n^2} \text{ eV}
where:
- 13.6 eV is the energy of the electron in the ground state (n=1).
- En represents the energy of the electron in the nth orbit.
The energy value is always negative, and the ground state (n=1) has the most negative energy.
Limitations
- It violates the Heisenberg Uncertainty Principle by treating electrons as having a known radius and orbit.
- The Bohr model calculates the ground state orbital angular momentum incorrectly.
- It predicts the spectra of bigger atoms incorrectly.
- The relative intensities of spectral lines are not predicted.
- Fine and hyperfine structures in spectral lines are not explained by the Bohr model.
- It does not account for the Zeeman effect.