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If
M
is the mass of the sample and
m
is the mass of a single atom of gallium, then
N
0
=
M
/
m
. Now,
m
= (67 u)(1.661
×
10
– 24
g/u) = 1.113
×
10
– 22
g
and
N
0
= (3.4 g)/(1.113
×
10
– 22
g) = 3.05
×
10
22
.
Thus,
R
0
= (8.89
×
10
– 3
h
– 1
) (3.05
×
10
22
) = 2.71
×
10
20
h
– 1
= 7.53
×
10
16
s
– 1
.
(b) The decay rate at any time
t
is given by
RR
e
t
=
−
0
λ
where
R
0
is the decay rate at
t
= 0. At
t
= 48 h,
λ
t
= (8.89
×
10
– 3
h
– 1
) (48 h) = 0.427 and
Re
=×
=
×
−−
−
7 53 10
4 91 10
16
1
0 427
16
..
.
.
ss
1
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 Spring '08
 Any
 Physics

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