Page 116 - Bruno Linder Elementary Physical Chemistry

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

Applications of Quantum Theory 101

2
∗
The quantity 4πr ψ ψ is the radial distribution function [sometimes
denoted as g(r)] and represents the probability of finding the electron
between r and r +dr in an atom.

Example 9.3.

(a) Calculate the radiation frequency, ν ∗ 1←4 , resulting from the transition
+
of n =4 to n = 1 in the Lyman Series of the spectrum of He .
(b) What is the probability of finding the He + electron within a volume
1
3
element δV =(1 pm) at a distance r = a o?
2
Solution

(a) The atomic number of He is Z =2, and so

2
2
2
5
ν 1←4 = Z R H (1/1 − 1/4 )= 4 × 1.097 × 10 cm −1 (1 − 1/16)
∗
5
=4.114 × 10 cm −1
2
3
(b) ψ δV =(1/π)(Z/a o ) exp(−2Zr/a o )δV

1
3
−11
=(1/π)(2/(5.292 × 10 m)) exp − 2 × 2 × (a o /a o)
2
× (10 −12 m) 3
=2.325 × 10 −6
9.7. Electron Spin

This is the intrinsic angular momentum of the electron. It may be thought
of as the electron spinning about its axis. Spin is a quantum mechanical
concept and the above classical analogue should not be taken too seriously.
An electron spin is characterized by a spin quantum number, m s ,which
can have the value 1/2 which means it spins in the clockwise direction,
or −1/2, which means it spins in the anti-clockwise direction. If the spin
quantum number is m s =1/2, the spin is often called α and denoted by an
upward pointing arrow ↑.If m s = −1/2 the electron spin is called β and
denoted by an arrow pointing downward, ↓.