Bohr’s Atom 185
The chemical properties of an atom are determined by the behaviour
of its electrons, principally the outer electron, which interact electro-
magnetically with the outer electrons of other atoms to form chemical
bonds. The electrons in the atom arrange themselves in shells. Each shell
corresponds to a different value of the principle quantum number, n. All
the electrons in a given shell have the same average radius, Rn. the
electrons in an atom under normal conditions settle into the state of
lowest energy, the ground state. The inner shells are therefore the first to
be filled. If it were not for the Pauli exclusion principle, all of the
electrons of an atom would be in the n = 1 shell. Because of the Pauli
exclusion principle, however, only a certain number of electrons are
allowed in each shell. First of all, only those states with orbital angular
momentum equal to l = 0, 1, ... , n – 1 are allowed in the n shell. For each
value of the orbital angular momentum, l, there are 2l + 1 possible values
of m corresponding to the 2l + 1 possible orientations of the plane of the
electron’s orbit. Since the quantum number ms can take on either the
value +1/2 or –1/2 corresponding to spin up and down, the Pauli
exclusion principle allows 2 × (2l + 1) possible states with the same
value of n and l. The n = 1 shell with only l = 0 states can therefore
accommodate 2 electrons whereas the n = 2 shell with l = 0 and l = 1
states can accommodate 2 + 6 or 8 electrons. The n = 3 shell, on the other
hand, with l = 0, l = 1 and l = 2 states can accommodate 2 + 6 + 10 or
18 electrons.
The first entry in the periodic table is the hydrogen atom with one
electron with n = 1, l = 0. The next entry, helium, has two electrons with
n = 1, l = 0 and opposite spins. The n = 1 shell is completed with helium
since this shell can only accommodate 2 electrons. This explains why
helium is an inert gas. The chemical properties of the atom are
determined by the electrons of the outer most shell. Since a closed shell
of electrons are extremely stable, those atoms whose outermost electrons
form a closed shell are chemically inactive and correspond to the inert
gases such as helium, neon, argon, etc. The hydrogen atom with only one
electron is, therefore, chemically quite active.
The third entry in the periodic table is lithium with 2 electrons in a
closed n = 1 shell and a third electron in the n = 2 shell with l = 0.
Lithium, an alkali metal, is extremely active chemically as are all the
other atoms, which consist of closed shells of electrons plus one extra
electron. These entries in the periodic table are also chemically
extremely active alkali metals such as sodium, potassium and cesium.