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516
Atomic Physics
Q42.6
From Equations 42.7, 42.8 and 42.9, we have
−=
−
=
+
−
=+
E
ke
r
r
r
KU
ee
e
e
22
2
. Then
KE
=
and
UE
e
=−
2.
Q42.7
Bohr modeled the electron as moving in a perfect circle, with zero uncertainity in its radial
coordinate. Then its radial velocity is always zero with zero uncertainty. Bohr’s theory violates the
uncertainty principle by making the uncertainty product
∆∆
rp
r
be zero, less than the minimum
allowable
=
2
.
Q42.8
Fundamentally, three quantum numbers describe an orbital wave function because we live in three
dimensional space. They arise mathematically from boundary conditions on the wave function,
expressed as a product of a function of
r
, a function of
θ
, and a function of
φ
.
Q42.9
Bohr’s theory pictures the electron as moving in a flat circle like a classical particle described by
Fm
a
∑
=
. Schrödinger’s theory pictures the electron as a cloud of probability amplitude in the
threedimensional space around the hydrogen nucleus, with its motion described by a wave
equation. In the Bohr model, the groundstate angular momentum is 1
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 Fall '11
 Staff
 Physics

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