Physics Asked on February 13, 2021
Is it possible for a hydrogen spectrum to show doublets and triplets?
My guess is that it is impossible as triplets and doublets are caused by the transition of electrons in having the same principal and azimuthal Quantum Numbers but different Magnetic Quantum Numbers (tell me I am right), but in the case of hydrogen since there is only a single electron it shouldn’t be possible, right?
The reason I am asking is that, in my textbook, it was stated that one of the reasons for the failure of the Bohr model of the atom was
It fails to account for the finer details (doublet, that is two closely spaced lines) of the hydrogen atom spectrum observed by using sophisticated spectroscopic techniques.
The only other explanation for doublets and triplets in hydrogen, in that case, would be that electron has made transitions between consecutive magnetic quantum numbers (e.g. in one hydrogen it goes from $p_x$ to $p_y$ and another from $p_y$ to $p_z$ and therefore a doublet is seen in the spectrum)
A single hydrogen atom has only one electron. Thus, it is in an (electronic) doublet state and there are no singlet or triplet states. The two states of the doublet are different in energy due to spin-orbit coupling. Basically, the electron can spin in the same direction as it is orbiting the nucleus or in the opposite direction. This is known as the fine structure and it is what your book refers to. This is not accounted for in the Bohr model because the Bohr model does not treat spin.
However, this is only the case if one neglects the spin of the nucleus. The spin of the nucleus can be parallel or anti-parallel to the spin of the electron leading to "triplet-like" or "singlet-like" states. The Bohr model does not account for this effect either. This is known as the Hyperfine structure.
Answered by Martin Peschel on February 13, 2021
It fails to account for the finer details also because it does not include any kind of relativistic correction and, also, it does not include any spin-related energy level. For example the hyperfine correction comes from considering the nucleus a magnetic dipole, and, not only, a point charge. So, the Bohr atomic model (since it can be solved exactly) is only the starting point from which you can try to reach a finer level of precision adding accurate corrections.
Answered by LDG on February 13, 2021
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