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()
U
9
1/2
UP
b
U
9
238/ 206
4.47 10 y
238
0.15mg
ln
ln 1
ln2
ln 2
206
0.86mg
1.18 10 y.
T
mm
t
m
⎡
⎤
⎛⎞
+
×
==
+
⎜⎟
⎢
⎥
⎝⎠
⎣
⎦
=×
For the
β
decay of
40
K, the initial mass of
40
K is
m
m
m
KK
A
r
K
A
r
0
40 40
=
+
=
+
/,
b
g
so
e
e
tt
0
K
KA
r
K
+
−−
λλ
b
g
.
We solve for
m
K
:
K
99
Ar
Ar
K
ln2 1
.1810 y/1
.2510 y
1.6mg
1.7mg.
11
1
t
me
m
m
ee
e
λ
−
−
××
=
=
−
63. We can find the age
t
of the rock from the masses of
238
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 Spring '08
 Any
 Physics, Mass

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