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55. (a) The charge that strikes the surface in time
∆
t
is given by
∆
q
=
i
∆
t
, where
i
is the
current. Since each particle carries charge 2
e
, the number of particles that strike the
surface is
N
q
e
it
e
===
×
×
=×
−
−
∆∆
22
025 10
30
216 10
23 10
6
19
12
..
.
As
C
ch
bg
c
h
(b) Now let
N
be the number of particles in a length
L
of the beam. They will all pass
through the beam cross section at one end in time
t = L
/
v
, where
v
is the particle speed.
The current is the charge that moves through the cross section per unit time. That is,
i
= 2
eN
/
t
= 2
eNv
/
L
.
Thus
N = iL
/2
ev
. To find the particle speed, we note the kinetic energy of a particle is
K
==
×
×
=
×
−−
20
20 10
160 10
32 10
61
9
1
2
MeV
eV
J / eV
J .
c
hc
h
Since
Km
v
=
1
2
2
,then the speed is
vK
m
=
2
. The mass of an alpha particle is (very
nearly) 4 times the mass of a proton, or
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This note was uploaded on 06/03/2011 for the course PHY 2049 taught by Professor Any during the Spring '08 term at University of Florida.
 Spring '08
 Any
 Physics, Charge, Current

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