1.3 Bohr’s theory 3Fig. 1.1The energy levels of the hydro-
gen atom. The transitions from higher
shellsn′=2, 3 , 4 ,...down to then=
shell give the Lyman series of spectral
lines. The series of lines formed by
transitions to other shells are: Balmer
(n =2),Paschen(n =3),Brack-
ett (n= 4) and Pfund (n= 5) (the
last two are not labelled in the figure).
Within each series the lines are denoted
by Greek letters, e.g. Lαforn=2to
n=1andHβforn=4ton=2.1.3 Bohr’s theory
In 1913, Bohr put forward a radical new model of the hydrogen atom
using quantum mechanics. It was known from Rutherford’s experiments
that inside atoms there is a very small, dense nucleus with a positive
charge. In the case of hydrogen this is a single proton with a single elec-
tron bound to it by the Coulomb force. Since the force is proportional
to 1/r^2 , as for gravity, the atom can be considered in classical terms as
resembling a miniature solar system with the electron orbiting around
the proton, just like a planet going around the sun. However, quantum
mechanics is important in small systems and only certain electron orbits
are allowed. This can be deduced from the observation that hydrogen
atoms emit light only at particular wavelengths corresponding to tran-
sitions between discrete energies. Bohr was able to explain the observed
spectrum by introducing the then novel idea of quantisation that goes
beyond any previous classical theory. He took the orbits that occur in
classical mechanics and imposed quantisation rules onto them.
Bohr assumed that each electron orbits the nucleus in a circle, whose
radiusris determined by the balance between centripetal acceleration
and the Coulomb attraction towards the proton. For electrons of mass
meand speedvthis gives
mev^2
r=
e^2
4 π 0 r^2. (1.3)
In SI units the strength of the electrostatic interaction between two