Page 114 - Bruno Linder Elementary Physical Chemistry

August 18, 2010 11:36 9in x 6in b985-ch09 Elementary Physical Chemistry

Applications of Quantum Theory 99

2) The azimuthal quantum number, l =0, 1, 2,..., which determines the
orbital angular momentum of the electron.
3) The magnetic quantum number, m l =0, ±1, ±2, ±3,..., which deter-
mines the angular momentum of an electron along a particular axis.

9.3. One-Electron Wave-Functions
One-electron wave-functions of hydrogenic atoms are called orbitals,and
are usually denoted by the symbols s, p, d, etc. representing l =0, 1, 2,
etc. preceded by a number which indicates the principal quantum number.
When l = 0, the orbital is denoted as s,when l = 1, the orbital is denoted
as p, etc. There are three different p’s — p x ,p y ,p z — which indicate the
directions.

Examples:
√
ψ 100 =(1/ π)(Z/a 0) 3/2 −Zr/a 0 ;1s (9.6)
e
√
ψ 200 =[1/(4 2π)](Z/a 0) 3/2 (2 − Zr/a 0 )e Zr/2a 0 ;2s (9.7)
√
e
ψ 210 =[1/(4 2π)](Z/a 0 ) 5/2 −Zr/2a 0 rcosθ;2p z (9.8)
9.4. Ionization Energy
The ionization energy is the maximum energy needed to remove an electron
from the ground state of an atom.
Example 9.2. Knowing that the ionization for H is I =13.9eV, what is
it for He + ?
Solution
2
+/E H = Z = 4, yielding for
Obviously, the only difference is Z,and so E He
+
He =4 × 13.59 eV = 54.36 eV.
9.5. Shells and Subshells

(a) In hydrogen and hydrogenic atoms, the energy depends only on the
principal quantum number n. In all other atoms, the energy depends
also on the quantum number l. It is standard practice to refer to
all electrons with the same n as belonging to the same shell.Often,
the shells are denoted by capital letters K,L,M,N,... , referring
respectively to n =1, 2, 3,...