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
In order to investigate this latter point we must look into the
formulæ for the revolutional frequency ω in a stationary orbit and for
the radiation frequency ν. Since, according to the Bohr theory, we
can apply the usual laws of mechanics to revolution in a stationary
orbit, it is an easy matter to find an expression for ω. From a short
mathematical calculation we can deduce that ω = R/_n_³, where R is
the frequency of revolution for the first orbit (_n_ = 1). We find
ν, on the other hand, by substituting in the Balmer-Ritz formula the
numbers _n_ and _n_ - 1, and a simple calculation shows that
for great values of _n_, the expression for ν will approach in the
limit the simple form ν = 2K/_n_³. For large orbit numbers,
ν accordingly varies as ω, _i.e._, inversely proportional to the
third power of n, and by equating R and 2K, we find that the values for
ν and ω tend more and more to become equal.
In this way the value of K, the Balmer constant, may be computed. It is
found that
_m_
K = 2π²_e_⁴-----
_h_³
where _e_ is the charge on the electron, _m_ the mass of the
electron, and _h_ is Planck’s constant. Upon the substitution
of the experimental values for these quantities, a value of K is
determined which agrees with the experimental value (from the spectral
lines investigation) of 3·29 × 10¹⁵ within the accuracy to which
_e_, _m_ and _h_ are obtainable. This agreement has
from the very first been a significant support for the Bohr theory.
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