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47. The fraction of undecayed nuclei remaining after time
t
is given by
N
N
0
=
e
−
λt
=
e
−
(ln 2)
t/T
1
/
2
where
λ
is the disintegration constant and
T
1
/
2
(= (ln 2)
/λ
) is the halflife. The time for half the original
238
U nuclei to decay is 4
.
5
×
10
9
y. For
244
Pu at that time,
(ln 2)
t
T
1
/
2
=
(ln 2)(4
.
5
×
10
9
y)
8
.
2
×
10
7
y
=38
.
0
and
N
N
0
=
e
−
38
.
0
=3
.
1
×
10
−
17
.
For
248
Cm at that time,
(ln 2)
t
T
1
/
2
=
(ln 2)(4
.
5
×
10
9
y)
3
.
4
×
10
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This note was uploaded on 11/12/2011 for the course PHYS 2001 taught by Professor Sprunger during the Fall '08 term at LSU.
 Fall '08
 SPRUNGER
 Physics

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