Bohr’s Atom 187
The next entry in the periodic table does not continue to fill the n = 3
shell by populating the l = 2 states as might be expected. Instead, the
two n = 4, l = 0 are populated in the next two entries, corresponding to
potassium and calcium. These two elements have the valencies +1, and
+2, respectively, since they have 1 and 2 electrons in excess of their
closed n = 3 (l = 0 and l =1) shell.
The n = 4, l = 0 states were filled before the n = 3, l = 2 states because
they are lower energy states in spite of the fact that their average radius is
larger than the n = 3, l = 2 states. Because the orbit of the n = 4, l = 0
states are much more elliptical than the n = 3, l = 2 whose orbit is
essentially circular, the n = 4, l = 0 electron penetrates the inner shells of
electrons and hence, feels the influence of the positive charge of the
nucleus more strongly. The electrons of the n = 3, l = 2 circular orbit, on
the other hand, are almost completely shielded from the positive charge
of the nucleus by the electrons of the inner shell. The magnitude of
potential energy of the n = 4, l = 0 electrons is greater, therefore, than
that of the n = 3, l = 2 electron. Since the potential energy of the
attractive force is negative, the total energy of the n = 4, l = 0 electrons is
less than that of the n = 3, l = 2 electron. The dependence of the energy
of the electron on the ellipsity of the orbit and hence, angular momentum
described above also explains why the l = 0 states are always filled
before the l = 1 states within the same n shell.
Once the two n = 4, l = 0 orbits have been filled, the n = 3, l = 2 orbits
are then populated, which accounts for the next ten entries of the periodic
table, scandium, titanium, vanadium, chromium, manganese, iron,
cobalt, nickel, copper and zinc. Each of these elements are metals that
are sharing many chemical properties, which are mainly determined
by their two n = 4, l = 0 electrons. The next 6 entries populate the n = 4,
l = 1 orbits producing another closed shell with krypton and completes
period 4 of the periodic table. Period 5 of the table repeats the pattern
of period 4, which the successive population of the two n = 5, l = 0
states, the ten n = 4, l = 2 states and finally the six n = 5, l = 1 states to
form another closed shell. Period 6 of the table is more complicated
consisting of 32 entries instead of the 18 entries of the two preceding
periods. The extra entries are due to the inclusion of the fourteen n = 4,
l = 3 states corresponding to the rare earth metals. The following states
are successively populated in period 6: the two n = 6, l = 0 states, the
fourteen n = 4, l = 3 states, the ten n = 5, l = 2 states and finally,