Radioactivity
description
Transcript of Radioactivity
Nuclear Physics, JU, Second Semester, 2010-2011(Saed Dababneh).
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Radioactivity
2
242
\2
42
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HeXX
XX
NAZN
AZ
2
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)( \ cmmQ
eXX
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NA
ZNAZ
2
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)2( \ cmmmQ
eXX
eXX
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fi
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Nuclear Physics, JU, Second Semester, 2010-2011(Saed Dababneh).
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Radioactivity
,...,,
)(
captureelectron
2
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nXX
NA
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Nuclear Physics, JU, Second Semester, 2010-2011(Saed Dababneh).
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Radioactivity
Natural decay series Other 2?HW 10HW 10
Nuclear Physics, JU, Second Semester, 2010-2011(Saed Dababneh).
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Radioactivity
Nuclear Physics, JU, Second Semester, 2010-2011(Saed Dababneh).
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Radioactivity
Nuclear Physics, JU, Second Semester, 2010-2011(Saed Dababneh).
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Radioactivity
Ndt
dN
≡ decay constant.
teNtN 0)(Compare to human life time!!!
Ndt
dN
693.02ln
21 t
Nuclear Physics, JU, Second Semester, 2010-2011(Saed Dababneh).
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Show that the mean lifetime .• N is difficult to measure.• Instead, measure N ≡ number of decays between t and t +t:
• If tt << << (i.e. << (i.e. << tt1/21/2)) then show that
and thus defining the activity A(t):
Radioactivity
693.02ln
21 t
1
)1(0)(
00ttttt eeNeNeNN
,0 teNN t
.)()( 00tt eAtAtNeN
dt
dN
)( 00 NA
Slope=?Slope=?!!!!!!!!!!!!!!!!!!!!
Be carefulBe careful..
?tAN
Nuclear Physics, JU, Second Semester, 2010-2011(Saed Dababneh).
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Radioactivity
HW 11HW 11Krane
Problem 6.1
• Activity measured in units of becquerel (Bq) = 1 decay/s.• 1 curie (Ci) = 3.7 x 1010 Bq.• Activity is not dose!!!!!
Nuclear Physics, JU, Second Semester, 2010-2011(Saed Dababneh).
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Radioactivity
Exponential decay of species 1 and exponential growth of species 2.
Isotope 1 (initial number N0) decays into “stable” isotope 2.
)1( 1
1
02
01
t
t
eNN
eNN
0)0(2
021
N
NNN
Nuclear Physics, JU, Second Semester, 2010-2011(Saed Dababneh).
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Radioactivity
• If parent nucleus decays by two modes:
Ndt
dN
Ndt
dN
bb
aa
NN
dt
dN
dt
dN
dt
dNtotalba
batotal
)(
ttotaleNtN 01 )(
)1(
)1(
0,2
0,2
t
total
bb
t
total
aa
total
total
eNN
eNN
0,2,21 NNNN ba
Derive.
Nuclear Physics, JU, Second Semester, 2010-2011(Saed Dababneh).
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Radioactivity
• If radioactive species 1 is produced in a reactor or accelerator with rate R.
Production Decay
111 NR
dt
dN Show that )1()( 1
11
teR
tN
and thus )1()()( 1111
teRtNtA
21
211
1 )(ttR
tttRtA
secular equilibrium
almost linear
HW 12HW 12
Nuclear Physics, JU, Second Semester, 2010-2011(Saed Dababneh).
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Radioactivity
• How long should we irradiate?• Activity per cost?
Nuclear Physics, JU, Second Semester, 2010-2011(Saed Dababneh).
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Radioactivity• If species 2 is radioactive.• Possible also that species 3 is radioactive.• 1 2 3 4 ….. until we reach a stable isotope.• But for now let us consider species 3 to be stable.• For the parent nucleus assume that N1(t=0)=N0.• For the daughters assume that N2(t=0) = N3(t=0) = 0.• Verify the following:
111 N
dt
dN 22112 NN
dt
dN
teNtN 101 )(
teNtNtA 101111 )()(
)()( 21
12
102
tt eeNtN
)()()( 21
12
210222
tt eeNtNtA
What if 2 = 0?
What if 1 is very small? N1(t) = ?
Nuclear Physics, JU, Second Semester, 2010-2011(Saed Dababneh).
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Secular equilibrium• 1 is very small (1 << 2) ►
• For large time t,A2 N01 which is the limiting value for secularequilibrium.
• Constant activity ►
production = decay.
)1()()( 210222
teNtNtA
022112 NN
dt
dN
Radioactivity
▼
2211 NN
What if t½ for 132Te were 78d?
Nuclear Physics, JU, Second Semester, 2010-2011(Saed Dababneh).
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Radioactivity
• Transient equilibrium• If 1 is smaller than 2 (1 < 2), show that
)1( )(
12
2
11
22
1
2 12 teN
N
A
A
Nuclear Physics, JU, Second Semester, 2010-2011(Saed Dababneh).
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Radioactivity
• As t increases,
but the activities themselves are not constant.
• 230Th decays, in effect, with the decay constant of 234U.
12
2
1
2
A
A
Parallel !?
Nuclear Physics, JU, Second Semester, 2010-2011(Saed Dababneh).
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Radioactivity
• Discuss the case when 1 is larger than 2 (1 > 2).
Nuclear Physics, JU, Second Semester, 2010-2011(Saed Dababneh).
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Radioactivity
• In general, 1 2 3 4 ….. until we reach a stable isotope.
• If N0 of type 1 and N2(t=0) = N3(t=0) = … = 0 ►Bateman equations.
iiiii NN
dt
dN 11
n
i
tin
iecNtA1
0)(
))...()((
......
21
321
mnmm
nmc
Exclude the term (k - k).