I'm talking about a neutral hydrogen atom here:
- According to Bohr, if the electron jumps from $n=2$ to $n=1$, there'd be only one wavelength of light being emitted. However, that is not the case we see experimentally. When an electron jumps from $n=1$ to $n=2$, more than one frequency of light, the values of which will be very close to each other (say $500nm$ and $500.01nm$) can be emitted. This is because, in the same shell, there are subshells, and some subshells have more energy than others. So, if the electron jumps from the $2s$ subshell to the $1s$ subshell, the emitted light's wavelength will be say $500.01nm$, and if the electron jumps from $2p$ to $1s$ the emitted light's wavelength will be say $500nm$. This is because the energy difference between $1s$ and $2s$ and $1s$ and $2p$ aren't the same. So, when an electron jumps from $n=2$ to $n=1$, there won't be a single line in the emission spectra as predicted by Bohr, rather there will be multiple fine lines very close to each other.
- Bohr's model can't explain the splitting of spectral lines into multiple fine lines under the influence of an electric or magnetic field. The spectral lines split because within subshells, there are orbitals, and they are differently oriented three-dimensionally. This has significant electromagnetic implications. For example, a $p$-subshell has three orbitals $p_x,p_y$ & $p_z$. They are differently oriented three-dimensionally, and as they have electrons moving in them, they have different electromagnetic orientations as well even though their energies are the same: they are degenerate orbitals. So, normally, in an emission spectrum, you don't notice any difference between $p_x,p_y$ & $p_z$ as they have the same energy, but under the influence of an electric or a magnetic field, you start to appreciate their individuality, as the lines emitted split. I think when observing the fine line of a $p$-subshell, if we apply an electric or a magnetic field, the line of the $p$-subshell will split into three finer lines with the same wavelength.
Questions:
- Is my explanation as a whole correct?
PS: In reality, there are no such things as shells or subshells. There are only orbitals. To make the learning curve less steep, teachers use these terms to high-school students like us.
Best Answer
Sentence n.1
Comparison of any theory with experimental values of spectral lines width is always a non-trivial task. This statement is true for Bohr's theory and Quantum Mechanics in the non-relativistic or relativistic formulation or even the full QED for the isolated H atom. There is the possibility, and actually, this is the case, that some important effect is not included. All the isolated atom mechanisms of broadening of the spectral lines of the Hydrogen atom in the absence of an external field are usually smaller than Doppler's and pressure broadening. The former is due to the doppler shift of the line frequency due to the spread of thermal velocities. The latter, also known as collision broadening, is due to the interaction between atoms when they get closer. Notice that both the effects would be present even at the level of Bohr's theory and would give a broadening of spectral lines larger than one order of magnitude in the majority of the experimental conditions.
The mechanism you are considering in your statement 1. is what one would call the intrinsic linewidth of the Hydrogen atom spectrum. In a complete QM treatment, its origin is due, as you correctly state, to the partial removal of the non-relativistic energy level degeneracy of the two opposite charges problem. Essential effects are due to the spin-orbit coupling (fine structure), electron spin-proton spin interaction (hyperfine structure), and QED effects (Lamb shift). However, this statement, too, would need a necessary correction. Indeed, removal of degeneracy would result in sharp lines with a small separation. Instead, even ignoring the spurious (but unavoidable) broadening due to the experimental finite resolution, there is always an intrinsic linewidth due to the finite time required by every electronic transition. According to the time-energy Uncertainty Principle, a transition occurring in a time $\tau$ would correspond to an intrinsic broadening $\Delta E$ not smaller than $\frac{\hbar}{\tau}$.
Sentence n.2
Shells and subshells are not equivalent to orbitals. They are just old names for energy levels. Similarly, the word orbital is just a different name for eigenfunction. Every orbital has corresponding energy, although one energy level may correspond to different orbitals. This is the degeneracy of the energy levels.
Within Bohr's theory there are no orbitals but quantized orbits. Apart from this warning, one can speak about energy levels and their degeneracy as in modern Quantum Mechanics. Actually, after Sommerfeld extended Bohr's ideas to elliptic orbits, the degeneracy of the energy levels was the correct one. The only problem is connected to the presence of the spin and its consequences. I think that in your statement 2. the presence of the spin should be mentioned explicitly.