Refinements of The Bohr Theory

Refinements of The Bohr Theory - Atomic structure and the periodic table

Chemistry Explain provides notes about Atomic structure and the periodic table today we discuss “Refinements of The Bohr Theory” Inorganic Chemistry.

It has been assumed that the nucleus remains stationary except for rotating on its own axis. This would be true if the mass of the nucleus were infinite, but the ratio of the mass of an electron to the mass of the hydrogen nucleus is 111836. The nucleus actually oscillates slightly about the center of gravity, and to allow for this the mass of the electron m is replaced by the. reduced mass µ in equation (1.4):

where M is the mass of the nucleus. The inclusion of the mass of the nucleus explains why different isotopes of an element produce lines in the spectrum at slightly different wavenumbers. The orbits are sometimes denoted by the letters K, L, M, N ... counting outwards from the nucleus, and they are also numbered 1, 2, 3, 4 ... This number is called the principal quantum number, which is given the symbol

Figure 1.4 Bohr orbits of hydrogen and the various series of spectral lines.

n. It is, therefore, possible t<> define which circular orbit is under consideration by specifying the principal quantum number. When an electron moves from one orbit to another it should give a single sharp line in the spectrum, corresponding precisely to the energy difference between the initial and final orbits. If the hydrogen spectrum is observed ~ with a high-resolution spectrometer it is found that some of the lines reveal 'fine structure'. This means that a line is really composed of several lines close together. Sommerfeld explained this splitting of lines by assuming that some of the orbits were elliptical; and that they precessed in space around the nucleus. For the orbit does to the nucleus, the principal quantum number n = 1, and there is a circular orbit. For the next orbit, #1e principal quantum number n = 2, and both circular and elliptical orbits ~re possible. To define an elliptical orbit, a second quantum number k is needed. The shape of the ellipse is defined by the ratio Of the lengths of the major arid minor axes. Thus

k is called the azimuthal or subsidiary quantum number and may have values from 1, 2 ... Ii. Thus for fl = 2, all may have the values 2/2 (circular orbit) and 2/1 (elliptical orbit). For the principal quantum number n = 3, nlk may have values 3/3 (circular),

3/2 (ellipse), and 3/1 (narrower ellipse). The presence of these extra orbits, which have slightly different energies k = 1 from each other, accounts for the extra lines in the spectrum revealed under high resolution. The original quantum number k has now been replaced by a new quantum number /, where I = k - 1. Thus for

This explained why some of the spectral lines are split into two, three, four, or more lines. In addition, some spectral lines are split still further into two lines (a double). This is explained by assuming that an electron spins on its axis in either a clockwise or an anticlockwise direction. Energy is quantized. and the value of the spin angular momentum was first considered to be ms· h/2n, where ms is the spin quantum number with values of ±~- (Quantum mechanics has since shown the exact expression to be Vs(s + I)· h/2n, where s is either the spin quantum number or the resultant of several spins.)
Zeeman showed that if atoms were placed in a strong magnetic field additional lines appeared on the spectrum. This is because elliptical orbits can only take up certain orientations with respect to the external field. rather than precessing freely. Each of these orientations is associated with a fourth quantum number m which can have values of l. (/ - I) .. . . 0 ... (-/ + I).-/. Thus a single line in the normal spectrum will appear as (2/ + 1) lines if a magnetic field is applied. Thus in order to explain the spectrum· of the hydrogen atom, four quantum numbers are needed, as shown in Table 1.2. The spectra of other atoms may be explained in a similar manner.