Energy levels Bohr formula

The great success of Bohr s model of Mendeleev s periodic table of the elements and the appUcabiUty of the Ritz formula for the energy levels show that treating the electron in an atom as if it were in a Coulomb field is a reasonable approximation. 

Here is an empirical constant now known as the Rydberg constant its value is 3.29 X 101J Hz. This empirical formula for the lines, together with the Bohr frequency condition, strongly suggests that the energy levels themselves are proportional to rg[n1. 

The energy levels generated by this formula are those you are all entirely familiar with. They are the Dirac energy levels. I need hardly say that a is the fine structure constant, now written as e2/ c[/i0c2/4x], that you will recognise k as (j +i) and discover that (k+w) has the same values as our present integer n, which is Bohr s n. 

We shall use these results in Section VII to obtain the Bohr formula for the energy levels of the hydrogen atom. 

Waerden, 1968) and can be used to rederive the Bohr formula for the energy levels. Corresponding to each energy level a unirrep of so(4) is obtained. The basis functions for each such unirrep are just the hydrogenic wave functions belonging to the energy level. 

The line of thought followed so far may be summarized as follows. Classical mechanics, on the basis of the picture of the electron revolving round the nucleus, certainly enables us to deduce formula) for the connexion between orbital radius, frequency of revolution, and energy, but it is incapable of explaining the spectrum emitted by the atom. Tor the latter purpose we have, following Bohr, to introduce a new hypothesis, viz. that the atom only possesses certain definite energy levels Bn = and it is the business of the new mechanics to... 

The explanation for these regular series lies in the existence of discrete, quantized energy levels. In 1913 Niels Bohr was able to derive the formula for these series in terms of the ad hoc quantum assumptions of the BOHR THEORY. In the mid-1920s the formula was derived in a deductive way from quantum mechanics. 

Bohr borrowed the idea of quantization of energy from Planck. Bohr, however, devised a rule for this quantization that could be applied to the motion of an electron in an atom. From this he derived the following formula for the energy levels of the electron in the hydrogen atom ... 

Using the Bohr formula for the energy levels, calculate the energy required to raise the electron in a hydrogen atom fi-om n= 1 to n = 00. Express the result for 1 mol H atoms. Because the n = 00 level corresponds to removal of the electron from the atom, this energy equals the ionization energy of the H atom. 

Calculate the ionization energy of the He" ion in kJ/mol (this would be the second ionization energy of He). See Problem 8.85. The Bohr formula for the energy levels of an ion consisting of a nucleus of charge Z and a single electron is... 

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