Limitations of Old Quantum Theory :
The quantum theory based on Bohr's quantum condition and Wilson-Sommerfeld quantum rule is known as old quantum theory. It is unable to explain some problems, e.g., energy states of hydrogen atom, particle in infinite square well, harmonic oscillator, etc. The main limitations of the old quantum theory are as follows:
(a) It is not applicable to non-periodic system.
(b) It cannot explain the relative intensities of the spectral lines.
(c) The spectral lines of hydrogen molecule and normal helium atom cannot be explained by this theory.
(d) The theory does not account the spin motion of the electron and the Pauli's exclusion principle.
(e) Even after applying the selection rule An ∆n' = ±1, Sommerfeld theory cannot gives the actual number of spectral lines.
(f) Sommerfeld method of elliptical orbits gives the correct total (n) of possible azimuthal quantum numbers but the actual values are incorrect. Spectroscopic studies reveals that the azimuthal quantum number can take the value zero so that the total values are 0, 1,2,. . ., (n–1). So a new azimuthal quantum number I is introduced where l = n'-1
A satisfactory explanation of the above difficulties has been provided by new quantum mechanics.
The quantum theory based on Bohr's quantum condition and Wilson-Sommerfeld quantum rule is known as old quantum theory. It is unable to explain some problems, e.g., energy states of hydrogen atom, particle in infinite square well, harmonic oscillator, etc. The main limitations of the old quantum theory are as follows:
(a) It is not applicable to non-periodic system.
(b) It cannot explain the relative intensities of the spectral lines.
(c) The spectral lines of hydrogen molecule and normal helium atom cannot be explained by this theory.
(d) The theory does not account the spin motion of the electron and the Pauli's exclusion principle.
(e) Even after applying the selection rule An ∆n' = ±1, Sommerfeld theory cannot gives the actual number of spectral lines.
(f) Sommerfeld method of elliptical orbits gives the correct total (n) of possible azimuthal quantum numbers but the actual values are incorrect. Spectroscopic studies reveals that the azimuthal quantum number can take the value zero so that the total values are 0, 1,2,. . ., (n–1). So a new azimuthal quantum number I is introduced where l = n'-1
A satisfactory explanation of the above difficulties has been provided by new quantum mechanics.
We will talk about the New Quantum Mechanics later in our website.
 |
| Sommerfeld elliptic orbit of the electron with the nucleus at one focus |