Quantum orbital

If we admit the hypothesis 2 that the three quantum orbits of the second series may contain a maximum of 6, 6 instead of 4, 4 electrons, it follows that PC15 also, and other quinquevalent compounds, may be written with ordinary valencies or duplet bonds only, giving shells of 10 . If, however, 8 is the maximum possible (failing the completion of 12), then PC16 must be constituted either as NII4C1, or it must contribute two electrons to a pair of chlorine atoms, thus developing a mixed bond. In the first case... 

For comparison, we now study the classical control problem and determine the field from Eq. (31), where the expectation values are replaced by the values of the classical coordinates and momenta, respectively. This yields the classical trajectory shown in Fig. 16, which is superimposed on the potential energy contours. Here, a perfect transfer is found where the particle stops in the minimum of the target potential well. A comparison with the trajectory derived from the quantum calculation (Fig. 14) shows that the classical orbit follows the quantum orbit closely until the reaction barrier is passed. At later times, due to the missing dispersion in the classical treatment, deviations are found. 

This gives for the work done in separating the electron when in the one-quantum orbit... 

It is not necessary here that n(0 should be integral, but it is the sum of the action integrals of the largest possible mechanical (not quantum) orbit divided by h. One obtains consequently... 

According to Kossel the emission lines are caused by an electron falling in from a higher quantum orbit to replace the ejected electron, whereby the energy of the atom decreases. Further, an electron from a still higher quantum orbit can fall into the vacated place until finally the last gap will be filled by a free electron. 

For Na(Z=ll) the value is 10-1, for Rb(Z=37) it is 36-3, and for W(Z=74) it is 76 5. We associate therefore the first K-line with the transition of an electron from a two-quantum to a one-quantum orbit. This suggests associating the remaining K-lines with transitions from higher quantum orbits to a one-quantum orbit. The K-lines have actually the theoretically required limit... 

The principle of linear increase of Vv is valid also for the L-lines. We attempt to identify these lines as transitions to a two-quantum orbit (n—2), and obtain for one of the L-lines the approximate wave number... 

In order to represent the numbers of electrons occupying the quantum orbits with different n, a two-dimensional diagram must be employed, for in order to include all the elements together with all their ions down to the bare nucleus the values of n must be shown as a function of both the atomic number Z and of the numbers of electrons z. An illustration of the ideas in question is provided by fig. 19, in... 

The expansions of the cartesian co-ordinates as functions of the angle variables (to be calculated from (26), 22) must now be introduced, to provide a starting-point for the calculation of the perturbations. In this connection, however, there is one point to be borne in mind. In the unperturbed Kepler motion (without taking account of the variation in mass) only Jx is fixed by the quantum theory, whilst J2, i.e. the eccentricity, remains arbitrary in the relativistic Kepler motion, J2 is also to be quantised and, for a one-quantum orbit, J2=J1=A. We shall not take account quantitatively of the relativistic variation of mass, but we shall assume that the initial orbit of each electron is circular with limiting degeneration J1=A,... 

If these maximum numbers of occupation be regarded simply as given, then the order of addition of the quantum orbits becomes, to a certain degree, comprehensible. We must suppose that the addition of a fresh electron to an already existing configuration takes place in such a way that the electron finally enters that quantum orbit in which it has the least energy (in which it is most firmly bound), and that it remains in this orbit during the capture of subsequent electrons. And here it must be borne in mind that an atom... 

If we calculate the radius of an orbit from the above equations, we find that it contains as a factor the square of the quantum number of the orbit, as well as other quantities. This means that the orbits having the same quantum number do not differ very much in radii, but that when the quantum number changes there is a considerable difference in radii. In the above distribution of electrons four orbits have quantum numbers of two, and four have quantum numbers of three. The radii of the two quantum orbits do not differ very much from each other, and the radii of the three quantum orbits do not differ very much from eadi other, but the latter are much larger than the former. It follows from this that the... 

Bohr has recently suggested an arrangement of orbits, one outside the other, that differs slightly from the arrangement adopted in the preceding calculations. He assumes that the three quantum orbit or orbits lie between the two quantum orbits, and that for those dements which have four Quantum dectrons the four quantum orbits lie between the two three quantum orbits. This arrangement of dectrons may be represented by the scheme... 

In order to make the computations for chemical elements other than those in table 3 it appears to be necessary to make additions assumptions as to just how the elements are built up in increasing values of the atomic numbers. There is also some difficulty about the radii of the various orbits. In general, a two quantum orbit has a much smaller radius than a three quantum orbit. 

It may be, also, that orbits that are not circular would give better values than circular orbits. Computations of the frequences on this basis present formidable difficulties. The fact, however, that the two quantum and three quantum orbits lie not in a plane, but in space of three dimensions may explain the appearance of three critical absorption wave-lengths in the L series, and six critical absorption wave-lengths in the M series, etc. 

At this point worth noting that, for a given n, there is only one maximum when the quantum orbital number takes its largest value ... 

This may be interpreted as evidence that aU elements containing more than two valency electrons have two electrons, which, further interpreted in terms of orbits, indicates that that two electrons in the outer structure of atoms are in quantum orbits the energies of which are different fiom that of other outer... 

Be sure you know what quantized means. Also understand the difference between a Bohr orbit (a fixed path the election travels around the nucleus) and the quantum orbited (a mathematically defined region in space in which there is a high probability of finding the electron). 

---