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Physics 21
Fall, 2004
Solution to HW28
38
P31
Calculate the wavelength of a 0.21 kg ball traveling
at 0.1 m/s.
λ
=
h
p
=
h
mv
=
6
.
63
×
10

34
0
.
21
×
0
.
1
=3
.
2
×
10

32
m
38
P32
What is the wavelength of a neutron (
m
=1
.
67
×
10

27
kg) traveling at 5
.
5
×
10
4
m/s?
λ
=
h
p
=
6
.
63
×
10

34
(1
.
67
×
10

27
)(5
.
5
×
10
4
)
=7
.
2
×
10

12
m
38
P36
Show that if an electron and a proton have
the same nonrelativistic kinetic energy, the proton has the
shorter wavelength.
Use the nonrelativistic relation between kinetic energy
E
,
momentum
p
, and mass
m
:
E
=
p
2
2
m
⇒
p
=
√
2
mE.
Then
λ
=
h
p
=
h
√
2
mE
For equal energies
E
, the larger mass of the proton will lead
to a smaller de Broglie wavelength.
39
P3
A proton is traveling with a speed of (4
.
825
±
0
.
012)
×
10
5
m/s.
With what maximum accuracy can its
position be ascertained?
The value of ∆
p
is the range of likely values of
p
,and
∆
p
=
m
∆
v
. We take ∆
v
=0
.
024
×
10
5
m/s (the full range
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 Fall '07
 Hickman
 Physics, Photon

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