Short Answer

The limitations refer to the weaknesses of the Bohr atomic model. Although the model explained the hydrogen atom successfully, it failed for atoms with more than one electron. It could not describe the spectra of complex atoms or explain the fine details seen in atomic spectra.

The model also ignored the wave nature of electrons and did not agree with modern quantum mechanics. Because of these limitations, the Bohr model was later replaced by the quantum mechanical model of the atom.

Detailed Explanation :

Limitations of the Bohr model

The Bohr model was an important development in atomic physics, but it had several limitations that made it incomplete. While the model successfully explained the stability of the hydrogen atom and its spectral lines, it could not describe the behaviour of more complex atoms. Many experimental discoveries also showed that Bohr’s assumptions did not fully match the true nature of electrons. As a result, the model was eventually replaced by the modern quantum mechanical model, which provides a more accurate understanding of atomic structure.

Bohr’s theory was based on the idea that electrons revolve around the nucleus in fixed circular orbits and that each orbit has a definite energy. Although this helped explain some observations, later studies revealed that electrons behave differently from what Bohr suggested. Electrons show both particle and wave nature, and their motion cannot be described using simple circular paths. Quantum mechanics later provided a more accurate explanation using probability distributions and orbitals instead of fixed orbits.

Major limitations of the Bohr model

1. Failed for multi-electron atoms
   The biggest limitation of the Bohr model is that it only works for the hydrogen atom and hydrogen-like ions (with one electron). For atoms with more than one electron, the model cannot explain their spectra or structure. Interactions between electrons make the system more complex, and Bohr’s simple assumptions do not work.
2. Could not explain fine structure in spectral lines
   When spectral lines of hydrogen were studied more closely using advanced instruments, they were found to be split into several closely spaced lines. This splitting is called fine structure. The Bohr model predicted only one line for each transition and could not explain why multiple lines appear.
3. Ignored electron spin
   The Bohr model did not include the concept of electron spin. Later research showed that electrons have an intrinsic property called spin, which affects their energy and causes additional splitting of spectral lines. Without considering spin, the Bohr model is incomplete.
4. Failed to explain the Zeeman effect and Stark effect

• Zeeman effect: splitting of spectral lines in the presence of a magnetic field
• Stark effect: splitting of spectral lines in an electric field

The Bohr model could not explain these effects because it assumed only simple circular orbits and did not include magnetic or electric interactions on electrons.

5. Did not satisfy the Heisenberg uncertainty principle
   The Heisenberg uncertainty principle states that the exact position and momentum of an electron cannot be known at the same time. Bohr’s model assumes fixed circular orbits with known positions and speeds, which directly contradicts this principle.
6. Could not describe elliptical orbits
   Experiments and advanced theories showed that electrons do not always move in circular paths. In the Sommerfeld model, electrons move in elliptical orbits. Bohr’s model was too simple to explain this behaviour.
7. Ignored the wave nature of the electron
   De Broglie proposed that electrons behave like waves. This wave nature creates standing wave patterns in atomic orbitals. Bohr’s model did not consider waves and treated electrons only as particles. This made the model incompatible with later discoveries in quantum mechanics.
8. Could not explain chemical properties of elements
   Chemical properties depend on the arrangement of electrons in atoms. The Bohr model does not explain why elements form different types of bonds or react differently. It gives only a basic idea of shells but not a full understanding of electron configuration.
9. Failed to explain intensity variations in spectral lines
   Spectral lines differ in brightness and intensity. Bohr’s model could predict wavelengths but not intensities. Quantum mechanics later solved this using probability distributions and transitions.

Why these limitations led to a new model

Because of these limitations, scientists realised that a new, more advanced model was needed. Quantum mechanics replaced Bohr’s simple orbits with orbitals, which describe regions where electrons are likely to be found. Schrödinger’s wave equation, Heisenberg’s uncertainty principle, and Pauli’s exclusion principle together created a complete model of the atom.

The quantum mechanical model explains:

• multi-electron atoms,
• shapes of orbitals,
• chemical bonding,
• spectra of all elements,
• fine structure,
• spin effects,
• behaviour in magnetic and electric fields.

This shows that although Bohr’s model was a major step forward, it was only a stepping stone toward the deeper and more accurate quantum theory.

Conclusion

The Bohr model has several limitations, such as failing to explain multi-electron atoms, fine structure, spin, and magnetic or electric field effects. It also contradicts the uncertainty principle and ignores the wave nature of electrons. While the model was successful for hydrogen, it was too simple for complex atoms. These limitations led to the development of the quantum mechanical model, which gives a complete and accurate description of atomic structure.