bei48482_FM

Quantum Theory of the Hydrogen Atom 209

Since the orbital kinetic energy of the electron and the magnitude of its angular

momentum are respectively

KEorbital m^2 orbital Lmorbitalr

we may write for the orbital kinetic energy

KEorbital

Hence, from Eq. (6.20),



Ll(l 1 ) (6.21)

With the orbital quantum number lrestricted to the values

l0, 1, 2, , (n1)

The electron can have only the angular momenta Lspecified by Eq. (6.21), Like to-

tal energy E,angular momentum is both conserved and quantized. The quantity

1.054 10 ^34 J s

is thus the natural unit of angular momentum.

In macroscopic planetary motion, as in the case of energy, the quantum number

describing angular momentum is so large that the separation into discrete angular

momentum states cannot be experimentally observed. For example, an electron (or,

for that matter, any other body) whose orbital quantum number is 2 has the angular

momentum

L2(21) 6  

2.6 10 ^34 J s

By contrast the orbital angular momentum of the earth is 2.7  1040 J s!

Designation of Angular-Momentum States

It is customary to specify electron angular-momentum states by a letter, with scorre-

sponding to l0, pto l1, and so on, according to the following scheme:

l (^0123456)
spdfghi
Angular-
momentum states
h

2 
Electron angular
momentum
^2 l(l1)

2 mr^2
L^2

2 mr^2
L^2

2 mr^2
1

2
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