CHAP. 12: BASIC TERMS OF CHEMICAL PHYSICS [CONTENTS] 431
the relation (12.36), and the energy change of the transition between different quantum states
is thus
∆E=μe^4
8 ε^20 h^2(
1
n^21−
1
n^22)
, (12.45)wheren 1 andn 2 are the principal quantum numbers of the states between which an electron
jump occurs. The energy of the emitted or absorbed photon is equal to the above change of
the atom energy. If we substitute (12.45) into (12.44), we obtain for the radiation wavenumber
ν ̃=RH(
1
n^21−
1
n^22)
, (12.46)where
RH=μ e^4
8 ε^20 h^3 c= 1. 09737 × 105 cm−^1 (12.47)is theRydberg constantfor the hydrogen atom. Individual wavenumbers for the constant
quantum numbern 1 are arranged in aspectral line seriesof gradually increasing values
approaching a limit. TheLyman series(n 1 = 1) lies in the ultraviolet region of the spectrum,
theBalmer series(n 1 = 2) can be found in the visible region, whereas thePaschen(n 1 = 3)
and other series lie in the region of infrared radiation. Each series limits to theseries edgeas
n 2 →∞. The series edge corresponds to the dissociation energy of the electron.
Other atomic spectra are substantially more complex, owing to the complexity of the en-
ergy levels of multielectron atoms. They are nevertheless composed of individual lines. Their
positions and intensities are characteristic for each atom and consequently allow for the iden-
tification of elements using spectroscopic methods.
In addition, electron transitions may occur in multielectron atoms between the inner and
excited electron levels. These transitions correspond to substantially higher energy changes, so
that the frequency of the corresponding radiation is in the X-ray region of the spectrum. For
the wavenumber we have the relation
ν ̃=RH(Z−σ)^2(
1
n^21−
1
n^22)
, (12.48)whereZis the atomic number of the element andσis a constant corresponding to the given
series. The preceding relation can be rewritten into the form of theMoseley’s law
√
̃ν=a Z+b , (12.49)