The Bohr Model of Hydrogenic Ions

The Bohr Atom 4
This value agrees very well with the observed wavelength of the Lyman- α line, 1215.7 A, °
indicating that the Bohr model may have some validity. But there still remains a thorny
problem. If the electron radiates energy as it moves in its orbit, the electron must loose energy,
and therefore spiral inward toward the nucleus, eventually collapsing. Thus, this picture is not
complete.
In an attempt to circumvent this classical collapse, Bohr looked to the findings of
Einstein and Planck. Since the energy of electromagnetic waves seem to come in packets of
size 2/ , Bohr postulated that the energy emitted from an atom must be emitted in dicrete
chunks of energy equal to 2/ . Thus, Bohr postulated that an electron could exist is some
orbiting state within the atom without radiating, but if the electron were to change from one
stable state to another, the energy change in the atom must be equal to the energy emitted by
the photon, or
I I œ 2
0 3 / (1.11)
To continue this line of reasoning, we must look for an expression for the total energy of
the atom. This is accomplished by combining the kinetic energy of the electron and the
electrostatic potential energy of the atom. The kinetic energy of the electron is related to the
electrostatic force by Equation 1.6, from which we can write
The electrostatic potential energy of the electron is given by
which gives
" 5Ð^/Ñ/
7@ # œ
(1.12)
# # <
Y Ð