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680 Periodic Table (Chemistry)

127.60) and iodine (I, atomic number 53, atomic mass value of l: m l = 0, ±1, ±2,..., ±l. Physically, the vari-
126.905) and for cobalt (Co, atomic number 27, atomic ous values of the magnetic quantum number indicate the
mass 58.9332) and nickel (Ni, atomic number 28, atomic possible values of the quantized z component of the angu-
mass 58.69). lar momentum of the electron. This means that m l deter-
mines the spatial orientation of the corresponding electron
C. Quantum Numbers, Electron
cloud. Each distinct orientation is termed an atomic or-
Shells, and Atomic Orbitals
bital, or simply an orbital. The spin quantum number, m s ,
The atomic number determines the identity of an element completes the set of four. It can assume only two possible
because the chemical properties of an element are almost values, +1/2 and −1/2. This differentiation takes into ac-
exclusively due to its electrons. The quantum mechanical count the fact that an electron can be regarded as spinning
model, which was first proposed in the 1920s, treats either clockwise or counterclockwise.
matter as if it had wavelike characteristics. Solution of
D. Building Up the Elements: Electron
the Schr¨odinger wave equation for an atom yields a set
Configurations
of mathematical wave functions that can be related to
the probabilities of locating the electrons both spatially The rules governing the relationships among the four
and energetically. This function, when plotted in three- quantum numbers are used in the “buildup” of the ele-
dimensional space, generates a probability cloud. We can- ments. We start with the simplest atom, hydrogen, and
not be absolutely certain where the electron will be at any successively add electrons to generate new atoms and ele-
instant, but we do know the region of space that is most ments. This process is guided by the Pauli Exclusion Prin-
probably occupied over time. ciple which states that no two electrons in the same atom
The wave functions include four quantum numbers that canhaveidenticalsetsofallfourquantumnumbers.There-
emerge from the calculation. These numbers, in effect, fore, as electrons are added, each is assigned a unique set
provide a unique energetic and spatial “address” for each of n,l, m l , and m s . The order of assignment is dictated by
electron in an atom. Such information, in turn, helps in- increasing energy. For each successive atom, the most sta-
crease our understanding of chemical properties and pe- bleelectronicarrangement(orgroundstate)isthatwiththe
riodicity. The principal quantum number, symbolized n, lowest energy. In general, the energy of an electron follows
is the chief indicator of the energy of the electron and the the sequence of increasing values for n and l, but there are
size of the electron cloud—in other words, how far, on the exceptions that manifest themselves in the periodic table.
average, the electron is from the nucleus. This number can The lowest energy level available to the single electron in
take on positive integer values: 1, 2, 3, etc. The fact that n a hydrogen atom is characterized by n = 1,l = 0, m l = 0,
can only have whole number values means that the energy and m s =±1/2 (the value of the spin quantum number is
of the atom is restricted to certain values, just as Bohr as- of no energetic consequence in this case). The electronic
sumed in his model for the hydrogen atom. Electrons with configurationisdesignated1s forn = 1ands forl = 0.The
the same value for the principal quantum number are said electron can occupy other orbitals, corresponding to other
to be in the same shell or level. values of n,l, and m l , but these represent “excited” states
The angular momentum of the electron is also quan- of higher energy. Next comes helium, with atomic num-
tized, and the azimuthal quantum number, l, specifies the ber 2. Its two electrons share the same values for the first
permissible values. The number l can assume integer val- three quantum numbers: n = 1,l = 0, m l = 0. However, in
ues between zero and (n − 1). Each value of l represents conformity with the Pauli Principle, they must differ in
a subshell or sublevel of the principal shell. These sub- m s . Thus, m s =+1/2 for one of the electrons and −1/2
shells are usually identified by an alphabetical code based for the other. Since both electrons in a helium atom are in
on old spectroscopic terms. Thus, l = 0 is designated an the n = 1,l = 0 orbital, the ground state for the element
2
s sublevel, l = 1 is called a p state, l = 2 is symbolized is written 1s with the superscript indicating the double
as d, l = 3 corresponds to an f subshell, and so on in al- occupancy. Note that these two sets of quantum numbers
phabetical order. The electronic distributions associated are the only possible sets for which n = 1. This, then, is an
with various values of the azimuthal quantum number are electronic explanation for why hydrogen and helium are
also identified by this code. The designation is important the only members of the first row of the periodic table.
because l reflects the shape of these electron clouds. The electronic configurations of the second and third
A third number which emerges from the wave equa- row elements are shown in Table II. Since all possible
tion is the magnetic quantum number, m l . Its permissible combinations of quantum numbers for n = 1 were used in
integer values are determined by l. When l is 0, m l can the first row, the second row begins by letting n = 2. First,
only be 0; if l equals 1, m l can have values of +1, 0, the 2s shell fills in a manner similar to that of the first row.
or −1. In general, m l can assume 2l + 1 values for each Then, because for n = 2,l can equal 0 and 1, the 2p shell