The Bohr Atom
(for hydrogen and hydrogenlike atoms)
M
n
r
+

M
e
v
Positive nucleus w/ electron orbiting about in a circle (m will refer to electron mass unless
noted)
Classical physics says that the electron will radiate (lose energy) and fall into the
nucleus, but it doesn't.
Why this is so is answered by "old" quantum theory.
Bohr put forward four postulates of his mechanics:
(1)
an e

in an atom is only allowed certain energies known as stationary states
(2)
radiation is due to changes in stationary states
(3)
an e

moves in circular orbits
(4)
allowed states have angular momentum in multiples of nh/2
π
Two important parameters may be derived given these postulates (radius, r, and energy, E).
The qualitative results of the model carry over into the modern version of q.m. so we will
examine it in detail.
First, we find an expression for r
angular momentum
≡
mvr, but by postulate 1, it is given by nh/2
π
∴
mvr = nh/2
π
(1)
the atom contains charged particles, so Coulombic forces must
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 Spring '09
 Electron, Nucleus, pH

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