PHYSICAL AND CHEMICAL PROPERTIES OF THE ELEMENTS 65
electromagnetic radiation which forms the basis, of Planck's theory
of temperature radiation. I shall not here go further into the
nature of these conditions but only mention that by their means
the stationary states are characterized by a number of integers,
the so-called quantum numbers. For a purely periodic motion like
that assumed in the case of the hydrogen atom only a single
quantum number is necessary for the determination of the stationary
states. This number determines the energy of the atom and also
the major axis of the orbit of the electron, but not its excentricity.
The energy in the various stationary states, if the small influence
of the motion of the nucleus is neglected, is given by the following
formula:
of temperature radiation. I shall not here go further into the
nature of these conditions but only mention that by their means
the stationary states are characterized by a number of integers,
the so-called quantum numbers. For a purely periodic motion like
that assumed in the case of the hydrogen atom only a single
quantum number is necessary for the determination of the stationary
states. This number determines the energy of the atom and also
the major axis of the orbit of the electron, but not its excentricity.
The energy in the various stationary states, if the small influence
of the motion of the nucleus is neglected, is given by the following
formula:
h n
m
where e and m are respectively the charge and the mass of the
electron, and where for the sake of subsequent applications the
charge on the nucleus has been designated by JSTe.
electron, and where for the sake of subsequent applications the
charge on the nucleus has been designated by JSTe.
For the atom of hydrogen JV"=1, and a comparison with
equation (3) leads to the following theoretical expression for K in
formula (2), namely
equation (3) leads to the following theoretical expression for K in
formula (2), namely
*-*£= ................... . ........ («)
This agrees with the empirical value of the constant for the spectrum
of hydrogen within the limit of accuracy with which the various
quantities can be determined.
of hydrogen within the limit of accuracy with which the various
quantities can be determined.
Hydrogen spectrum and X-ray spectra. If in the above
formula we put ^=2 which corresponds to an atom consisting of
an electron revolving around a nucleus with a double charge, we
get values for the energies in the stationary states, which are four
times larger than the energies in the corresponding states of the
hydrogen atom, and we obtain the following formula for the
spectrum which would be emitted by such an atom :
formula we put ^=2 which corresponds to an atom consisting of
an electron revolving around a nucleus with a double charge, we
get values for the energies in the stationary states, which are four
times larger than the energies in the corresponding states of the
hydrogen atom, and we obtain the following formula for the
spectrum which would be emitted by such an atom :
/= 48"
This formula represents certain lines which have been known for
some time and which had been attributed to hydrogen on account
of the great similarity between formulae (2) and (7) since* it had
some time and which had been attributed to hydrogen on account
of the great similarity between formulae (2) and (7) since* it had