The atom and the Bohr theory of its structure : $b an elementary presentationHolst, Helge
Science
The atom and the Bohr theory of its structure : $b an elementary presentation
Holst, Helge
Atomic theory
Before going farther we shall recall what has previously been said
about the quantum numbers. In the undisturbed hydrogen atom, the
stationary orbits can be numbered with the principal quantum numbers
1, 2, 3 ... _n_. But to each principal quantum number there
corresponds not one but several states, each with its auxiliary quantum
number 1, 2, 3 ... _k_, _k_ at the most being equal to the
principal quantum number. In a similar way, the stationary orbits of
the electrons in an atom containing several electrons can be indicated
by two quantum numbers, the 3₂ orbit, for instance, being that with
principal quantum number 3 and auxiliary quantum number 2. But while
in the hydrogen atom the principal quantum number _n_, in the
stationary orbits which are slowly rotating ellipses, is very simply
connected with the length of the major axis of the ellipse, and
_k_: _n_ is the ratio between the minor and major axes,
still in other atoms with complex systems of electrons the significance
of the principal quantum number is not so simple and the orbit of
an electron consists of a sequence of loops of more complicated
form (cf. Fig. 29). We must satisfy ourselves with the statement
that a definition of their significance can be given, but only by
mathematical-physical considerations which we cannot enter into here.
It may, however, be stated that, if we restrict ourselves to a definite
atom, the rule will hold that, among a series of orbits with the same
auxiliary quantum number but different principal quantum numbers, that
orbit in which the electron attains a greater distance from the nucleus
has the higher number. Another rule which holds is, that an orbit with
a small auxiliary quantum number in comparison with its principal
quantum number (as 4₁ for instance, cf. Fig. 29), will consist of very
oblong loops with a very great difference between the greatest and
least distances of the electron from the nucleus, while the orbit will
be a circle when the two quantum numbers are the same as for 1₁, 2₂,
3₃. Although each orbit has two quantum numbers, we often speak simply
of the 1-, 2-, 3- ... _n_-quantum orbits, meaning here the orbits
with the principal quantum numbers 1, 2, 3 ... _n_.
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