Limitations of Bohr’s Quantum Theory of Spectra

Even though Niels Bohr’s quantum theory of spectra was regarded as one of the most revolutionary and successful theory of atomic dynamics, it was limited in the following ways:

• It had only limited success in predicting emission and absorption wavelengths for multi-electron atoms.
• It failed to predict the observed intensities of spectra lines.
• It failed to provide an equation of motion governing the time development of atomic systems starting from some initial state.
• It did not supply a general scheme for “quantizing” other systems, especially those without periodic motion.
• It overemphasized the particle nature of matter and could not explain the newly discovered wave-particle duality of light.

To overcome some of these limitations, Louis Victor de Broglie hypothesized that because photons have wave and particle characteristics, perhaps all forms of matter have wave as well as particle properties. According to De Broglie electrons had a dual particle-wave nature. Accompanying every electron was a wave [not an electromagnetic wave], which guided or piloted the electron through space.

De Broglie concluded that the wavelength (λ) and frequency (f) of a matter wave associated with any moving object were given by:

λ = h/p and f = E/h

Where h is Plank’s constant, p is the relativistic momentum, and E is the total relativistic energy of the object.

De Broglie Explanation of the Quantization in the Bohr Model

Bohr’s model of the atom had many flaws. For instance, as the electrons revolve around the nucleus, how can we comprehend the fact that only particular electronic energies are allowed? Why do all atoms of a given element have precisely similar physical properties regardless of the infinite variety of starting velocities and positions of the electrons in each atom?

De Broglie acknowledged that even though there were issues with particle theories, wave theories of matter deals with these problems effectively by way of interference. For instance, a plucked guitar string, although initially subjected to a wide range of wavelengths, supports only standing wave (i.e. a stationary wave characterized by points of zero vibration and points of maximum vibration) patterns that have nodes at each end. Therefore, only a discrete set of wavelengths is allowed for standing waves, while other wavelengths not included in this discrete set rapidly vanish by destructive interference. This same logic can be employed to electron matter waves bent into a circle around the nucleus. Although initially a continuous distribution of wavelengths may be present, corresponding to a distribution of initial electron velocities, most wavelengths and velocities rapidly die off. The residual standing wave patterns thus account for the identical nature of all atoms of a given element and show that atoms are more like vibrating drum heads with discrete modes of vibration than like miniature solar systems.

You may also read:

• The Limitations of Classical Physics
• Quantum Mechanics vs. Newtonian Mechanics
• Hadrons vs. Leptons
• Bohr’s Correspondence Principle
• Einstein’s Special Theory of Relativity
• The Exclusion Principle