Nuclear Physics, JU, Second Semester, 2010-2011(Saed Dababneh).

1

Radioactivity

2

242

\2

42

)( \ cmmmQ

HeXX

XX

NAZN

AZ

2

\11

)( \ cmmQ

eXX

XX

NA

ZNAZ

2

\11

)2( \ cmmmQ

eXX

eXX

NA

ZNAZ

2

2

2mc

EEEEE

TEEE

fi

Rfi

Nuclear Physics, JU, Second Semester, 2010-2011(Saed Dababneh).

2

Radioactivity

,...,,

)(

captureelectron

2

\11

\

MLKn

BcmmQ

XeX

nXX

NA

ZNAZ

Nuclear Physics, JU, Second Semester, 2010-2011(Saed Dababneh).

3

Radioactivity

Natural decay series Other 2?HW 10HW 10

Nuclear Physics, JU, Second Semester, 2010-2011(Saed Dababneh).

4

Radioactivity

Nuclear Physics, JU, Second Semester, 2010-2011(Saed Dababneh).

5

Radioactivity

Nuclear Physics, JU, Second Semester, 2010-2011(Saed Dababneh).

6

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).

7

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).

8

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).

9

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).

10

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).

11

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).

12

Radioactivity

• How long should we irradiate?• Activity per cost?

Nuclear Physics, JU, Second Semester, 2010-2011(Saed Dababneh).

13

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).

14

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).

15

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).

16

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).

17

Radioactivity

• Discuss the case when 1 is larger than 2 (1 > 2).

Nuclear Physics, JU, Second Semester, 2010-2011(Saed Dababneh).

18

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).