Page 108 - Bruno Linder Elementary Physical Chemistry

August 18, 2010 11:36 9in x 6in b985-ch08 Elementary Physical Chemistry

Introduction to Quantum Theory 93

(a) At the nucleus, r =0 and

3
Prob = (8/πa ) × (1pm) 3
0
3
3
3
= {8/(π × 52.9 pm )}(1pm )
=1.72 × 10 −5
(b) At r = a 0,
2
3
Prob = (8/πa ) ×{exp (−2a 0/a 0 )} (1pm) 3
0
3
2
3
= {8/(π × 52.9 pm )}(exp − 2) pm 3
=3.15 × 10 −7
The probabilistic nature of quantum mechanics manifests itself in
(a) The Schr¨odinger formulation through the wave function.
(b) The Heisenberg formulation through the Uncertainty Principle,which
states that it is not possible to know with complete certainty both
the momentum and position of a particle. More precisely, if ∆p and
∆x represent respectively the uncertainty in momentum and the
uncertainty in position, then quantum theory requires that

∆p × ∆x ≥ h/4π (8.7)

8.7. Summary and Conclusions

(1) Quantum mechanics is probabilistic, unlike classical mechanics, which
is deterministic.
(2) The Copenhagen Interpretation. In 1927, the leading scientists met
at Lake Como for the purpose of arriving at some consensus of
the meaning of quantum mechanics. This resulted in an interpre-
tation, referred to as the Copenhagen Interpretation, because of
the leadership of Bohr. Most scientists of those days accepted the
Copenhagen Interpretation as the true meaning of quantum mechan-
ics. Einstein never did. Another notable scientist who had prob-
lems with some of the Copenhagen Interpretation was Schr¨odinger.

The most important conclusions of the Copenhagen Interpretation are
(a) The dual nature of light and of matter. They can exist either as
particles or as waves.