Parcleinaring inthespiritofthebohrsmodel

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Unformatted text preview: n2 ⎟ 2 2 ⎝i f⎠ n = 1, 2, 3, ... Radius
of
the
hydrogen
atom
ground
 state
(n=1)
 Ze2 In MKS units the electrostatic force is F = 4πε 0 r 2 4πε 0 2 4 ⋅ 3.14159265358979 ⋅ 8.854187816 ⋅ 10 −12C 2 J −1m −1 (1.05457266 × 10 −34 J ⋅ s )2 rn =1 = = 2 2 −31 −19 Zme 1 ⋅ 9.1093897 × 10 kg ⋅ −1.60217733 × 10 C ( = 5.2910424 ⋅ 10 −11 m = 0.52910424 ⋅ 10 −8 cm = 0.52910424Å C 2 J −1m −1 ( J ⋅ s )2 J ⋅ s 2 ⋅ m −1 ⎛ m 2 ⎞ s 2 ⋅ m −1 Unit analysis: = = ⎜ kg 2 ⎟ = m(eter ) 2 kg ⋅ C kg s ⎠ kg ⎝ 
 ) Bohr’s
model
 •  Main
assump,on:
Electron
angular
momentum
is
 quan,zed
mvr=nħ
 •  Problems: 

 –  Accelerated
electron
does
not
radiate
 –  Not
possible
to
model
more
than
one
electron
 –  Violate
uncertainty
principle

 Δx ⋅ Δp ≥ a0 n 2 r= Since
we
know
the
coordinate




















and
 Z momentum




















exactly
 p = n r The
wavefunc,on
(con,nue)
 –  The
total
probability
must
be
one.
 P ( x ) dx = ∫ ψ * ( x )ψ ( x ) dx = 1 ∫ –  The
wavefuc,on
and
its
first
deriva,ve
must
be
 con,nuous...
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