Homework 1
2.
We work from the definition of the frequency
and the wavelength
to give, for the electron,
Now, the phase and group velocities are
The proton is 1831 times heavier than the electron, and this affects the momentum
and therefore the de Broglie wavelength as
f
=
100
⋅
1.6
×
10
−
19
6.625
×
10
−
34
=
2.42
×
10
16
Hz
λ
=
6.625
×
10
−
34
⋅
1.673
×
10
−
27
⋅
1.6
×
10
−
17
=
2.85
×
10
−
12
m
and the velocities are now
v
ϕ
=
ω
k
=
2
π
f
2
/
=
f
=
6.91
×
10
4
m
/
s
v
gr
=
k
m
=
p
m
=
2
E
m
=
1.38
×
10
5
m
/
s
3.
We work with
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.
4.
If the electron has an energy of 100 eV, then the average momentum is
p
=
mE
=
5.4
×
10
−
24
.
The elapsed time is given as
t
=
2
m
σ
2
=
2
m
Δ
x
( )
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 Fall '09
 TSAKALIS
 Photon, Frequency, Fundamental physics concepts, Matter wave, corresponding photon energy

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