MadSci Network: Chemistry
Query:

Re: Did the Bohr Model have sub-levels?

Date: Tue Nov 11 12:42:12 2003
Posted By: Todd Whitcombe, Associate Professor, Chemistry
Area of science: Chemistry
ID: 1068260096.Ch
Message:

Your teacher is "right" - sort of. As postulated by Bohr, in his 1913 paper entitled "On the Constitution of Atoms and Molecules" the "Bohr Model" of the atom only contained a single quantum number. This principal quantum number, which we now routinely call "n", was the sole determinant of the energy of the stationary state of the electron. Changes in "n" represented changes in the energy of the system and it was through a combination of classical mechanics and inspiration into quantization that Bohr was able to make his leap forward:

"The principal assumptions used are :

(1) That the dynamical equilibrium of the systems in the stationary states can be discussed by help of the ordinary mechanics, while the passing of the systems between different stationary states cannot be treated on that basis.

(2) That the latter process is followed by the emission of a homogeneous radiation, for which the relation between the frequency and the amount of energy emitted is the one given by Planck's theory.

The first assumption seems to present itself ; for it is known that the ordinary mechanics cannot have an absolute validity, but will only hold in calculations of certain mean values of the motion of the electrons. On the other hand, in the calculations of the dynamical equilibrium in a stationary state in which there is no relative displacement of the particles, we need not distinguish between the actual motions and their mean values. The second assumption is in obvious contrast to the ordinary ideas of electrodynamics but appears to be necessary in order to account for experimental facts."

His theory explained the Balmer series - the line spectra of hydrogen. It did so using mostly classical mechanics. It did so using a single "entire" number (a single whole number) to represent the energy level of the stationary state of an electron. It provided a rational system for spectroscopy imposing order on chaos as J.J. Thomson put it. And it never mentioned the word orbital - just "stationary states" for electron energy.

But even Bohr, in his 1913 paper, recognized that it did not go far enough:

"The circumstance that the frequency can be written as a difference between two functions of entire numbers suggests an origin of the lines in the spectra in question similar to the one we have assumed for hydrogen; i.e. that the lines correspond to a radiation emitted during the passing of the system between two different stationary states. For systems containing more than one electron the detailed discussion may be very complicated, as there will be many different configurations of the electrons which can be taken into consideration as stationary states. This may account for the different sets of series in the line spectra emitted from the substances in question. Here I shall only try to show how, by help of the theory, it can be simply explained that the constant K entering in Rydberg's formula is the same for all substances."

So, strictly speaking, Bohr in formulating his model, left open the question of what it would mean for multi-electron systems. He recognized that the answer would be complex. It was for others ( Heisenberg, Dirac, Sommerfield, and Schrodinger) working with or in concert with Bohr to develop the full picture and build the electronic structure of the atom on the four quantum numbers. It did not take long. By 1921, a much better model had evolved - and it is this latter model that still gets called the "Bohr Model". Hence, when your teacher said that the "Bohr Model" doesn't have sub-levels, if he or she meant the model originally postulated by Bohr and presented in 1913, then he/she is absolutely correct. If he/she meant the model that rapidly emerged once Bohr had shown the way, then an argument could be made that he/she is not - but not a strong argument for the newly developed "Bohr Model" rapidly became the "Quantum Mechanical Model" and, for the most part, this is what you are being taught.

As to "s,p,d,f", these are not "sub-levels" but designations for the orbital angular momentum within a particular "n-shell" according to the quantum mechanically derived model of the atom. They arise from spectroscopy which showed that while Bohr's model worked, even the line spectra for hydrogen demonstrated fine structure. The letters mean: "s" sharp, "p" principal, "d" diffuse, and "f" fundamental. It was the fact that there was fine structure in the spectra of more complex atoms that necessitated the modification of the Bohr Model and ultimately to the development of the Quantum Mechanical Model of the atom.

Hope this answers your question.


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