A system of physical chemistry - Index of

loo A SYSTEM OF PHYSICAL CHEMISTRY

If we now suppose that the radiation in question is homogeneous,

and that the amount **of** energy emitted is equal to hv^ we get—

and hence

This expression gives the frequency **of** the homogeneous radiation

emitted by the gas when the atomic **system** changes from the stationary

state defined by ti to the stationary state defined by r^. If these two

states were the only possible ones the gas could only give rise to a single

frequency j'. The quantities t2 and tj are whole numbers, and a single

atom is capable **of** existing in a corresponding number **of** stationary

states, so that in general a number **of** lines will be emitted as is borne

out by experiment. The above expression is capable **of** accounting for

series **of** lines emitted by incandescent hydrogen. If we — put t^ 2

and allow t^ to vary, i.e. tj can take on the values 3, 4, 5, etc., we get

the well-known Balmer series **of** lines in the hydrogen spectrum. It is

noteworthy that to account for the Balmer hydrogen line spectra we

have to assume that the electron from an outer orbit passes to the

second orbit {t^ = 2) and not to the first or innermost orbit, which re-

presents maximum stability. If we put T2 = 3 and allow t^ to vary

(tj = 4, 5, 6, etc.), we get the infra-red series **of** lines observed by

Paschen {Ann. Fhysik, 27, 565 (1908)). If we put to = i and allow

Tj to vary we get a series in the extreme ultra-violet, the furthest Lyman

region. In the case **of** elements heavier than hydrogen, e.g. platinum,

the kind **of** radiation to be expected on putting T2 = i corresponds to

X-rays. If we put t^ = 4, 5, etc., we get series **of** lines in the extreme

infra-red not yet observed. It will be observed that Bohr's theory

accounts excellently for those series **of** lines which have been observed

in the case **of** hydrogen and is even capable **of** predicting other series

in regions not yet examined. Further, the agreement is quantitative

as well as qualitative. Putting e = 4*78 x lo"^** electrostatic units;

ejm = 5-31 X 10^'^; and /^ = 6-55 x lo"^'^, we get—

2ir'~me^

h^

3'26 x 10^^,

whilst the value obtained experimentally for the factor (the so-called

Rydberg constant) outside the bracket in formula (4) is 3*290 x lo^^.

The agreement between the observed and calculated value is within the

error due to experimental determination **of** the various quantities in-

volved.

It may be pointed out that it has not been possible to observe more

than twelve lines **of** the Balmer series in experiments with vacuum tubes

whilst thirty-three lines are observed in the spectra **of** certain celestial

bodies. This may likewise be anticipated on the basis **of** Bohr's

theory. According to equation (3) the diameter **of** the orbit **of** the