Radioactivity and radiation. .(radiaoactivity) ) Decay (Disintegration ... α - decay

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1 Radioactivity and radiation ) -(.(radiaoactivity) ) Decay (Disintegration α - decay 2 2 3

2 ( ) U Th α. : U Th + 4 2He (α) Pb 82 Po : Po Pb + α ) (daughter nucleus) Parent nuvleus.( : M p ( M d + M α ) > 0 (2-1) M α M d M p

3 : E E = { ( M p ( M d + M α ) } C 2 (2-2) ( ). M d E E α M p : E α = ( M d / M p ) E (2-3).. ( 1-2). 5 β - decay 3-2.( β - particles)

4 (positron).. ( ). N αβ E α N β E β N β E β 6

5 - - :(1-2) + - 7

6 1 ( N/Z ) 1.6 ( 12 6C) = 6/6 = N/Z ( 14 6C)14. : N / Z = 8/6 = 1.33 ( Cs) 133 ( Cs) (2-2) Z N... ) 238 ) ( α. (α : 238 N/Z.234 N / Z = 146 / 92 = : 234 N / Z = 144 / 90 =

7 . : Th Pa + β ( ) N/Z (2-2) 9

8 Types of β-decay The electron decay : 1 0 n 1 1 p + β - ( 60 Co ) ( 137 Cs ) 137 ( 60 Ni) 60 :The positron decay.( 137 Ba ) -.. : 1 1 P 1 0 n + β + ( 22 Na ) 22.( 22 Ne ) 22 The electron capture -. ) ( L K. : 0

9 0-1 e P 1 0 n.(electron capture) (β + ) (β - ).. ( ) ν (neutrino). ( m ν =0 ) : ( ) 10n ( ) 1 1 P 0 ( ) -1 e + 1 1P 1 1 P + β - + ν 1 0n + β + + ν 1 0n + ν.(anti - neutrino) ν ).( :. A Z M > ( A Z+1 M + m e ) (2-4) A A m e Z+1 M Z M. : A Z M > ( A Z-1 M + m e ) (2-5) 1

10 A Z-1 M. : (m e + A Z M) > A Z-1M (2-6) (6-2) (5-2).. (6-2)..(5-2). Energy of β- particles β... : E = { A ZM - ( A Z+1M + m e )} C 2 (2-7) : E= { A ZM - ( A Z-1M + m e )} C 2 (2-8). :

11 E = ( A ZM A Z-1M ) C 2 (2-9). ( ).(end point)...( 1-2 ).. Gamma radiation 4-2 ).( excited state ( ).(ground state). 3

12 K ) ( (internal conversion). ( ) : Na e Na Ne * + β + : Ne * * ( ). ( 3-2). ( 3 2 ) : Co Ni * + β - + ύ 60 ( )

13 1.173.( ) 22 Na ( 3-2 ) Ne γ β + + EC 0 60 Co β γ γ 0 ( 3-2) Ni i E γ f : E γ = E i E f = hν 5

14 ν (. E f 34 E i 10x6.63 = h) h. The internal conversion M L K.. M L K.( 1-2) ( ) M L K. K.M L

15 ... E e = E γ Be E γ E e. B e E e = = 329 KeV K :. K ( ) L 8.9 : L E e = = KeV. ) K L. M L K. K K α k 7

16 . 1 α k. Z M L. K.. X - rays 5-2. : ( ). ( )..

17 ( )... K L L M. K. L. K α1 K L 3 ( ) K L 2 ) (4-2). K α2 (. :.. M3 2P3/2 M2 2P1/2 M1 2S1/2 L3 2P3/2 L2 2P1/2 L1 2S1/2 K 1S1/ : 9

18 . K L 3 : 82Pb K α1 K α1 (L 3 > K ) = = KeV K α2 ( L 2 > K ) = = KeV K β1 = ( M 3 > K ) = = KeV K β2 = ( M 2 > K ) = = KeV M V M 1V M 111 M 1 M 11 L 111 L α1 L β1 L α2 L 11 L 1 L 1 K K α1 K α2 K β3 K β1 0

19 (4-2) ( ) ( ).. (5-2). ( ). N x 1 E x

20 :(5-2) 2

21 Auger electrons ) (1-5-2) M L K (... K K L. L.L M.M.. M : E e = h ν E M E e L = E K E L - E M h ν.k.. KLM 3

22 M K L M. K L M ω K K. K The radioactive decay The radioactive decay law ( ) : 0 < λ < < 1 dt N. (λ dt). N λ dt dt : dn = - N λ dt 4

23 N N. N 0 t = 0 : N (t) = N 0 e - λ t (2-10) N(t). t ( ) λ The sample activity A(t).(10-2).(Activity of a Sample) : (10-2) A(t) = dn(t) / dt t = 0 = λ N 0 e - λ t = λ N(t) (2-11) A 0 = λ N 0 A(t) = A 0 e - λt (2-12) : The half-life and mean-life ( ).. 5

24 t = t 1/2 N(t) = N o /2. t 1/2 : (10 2) -λ t1/2 N 0 / 2 = N 0 e t 1/2 = ln 2 / λ : λ = / λ (2-13) 1-.( ) /1 τ ( ) : (10-2) τ = (1 / N 0 dn(t).t = 1/ λ = t 1/2 / (2-14) τ 0 t 1/2 λ. t 1/2 λ λ (12-2) ln {A(t) / A 0 } = - λ t.( e = 2.71 ) (ln) : log {A(t) / A 0 } = λ t (2-15) 6

25 = : log A(t) = log A λ t (2-16) t log A(t). S = λ ( 6-2 ).λ t 1/2.(14-2) (13-2) τ λ ( ). (counting rate) R ) R ( : R(t) / R 0 = A(t) / A 0 log A t t ( 6-2 ) log A 7

26 λ.. (16-2) λ A 0 λ = { log A 0 log A(t) }/ t. t A(t) R(t).(12-2) t [R(t) α A(t)] R(t) t 1/2 (7-2). 2 = (2/1) 7 (4/1) 7 ( 128/1 ) = (2/1) 10 %0.1 (1024/1) = (2/1 ).. λ t 1/ ) 9 ( 10 x

27 :. dn / dt = λ N = A = R / C C R N C R. λ R 0 ½ R 0 ¼ R 0 t 1/2 2t 1/2 3t 1/2 t t (7-2) R(t) ( ) 9

28 . R(t). t log R a. t log R (8-2) log R 4 a b 2 c t t (8-2) log R (8-2). b a b. 0

29 c a.. λ 2 The successive radioactive decay λ (grand-daghter).. )226 3 ).222 ( 10 x ( 3.82.( 3.05 ) ( ) N 1 t N 2 λ 1 N 3 λ 2 t = 0 : N 1 = N 10, N 2 = 0, N 3 = 0 (11-2) 1

30 : d N 1 / d t = - λ 1 N 1 (2-17) d N 2 / d t = λ 1 N 1 λ 2 N 2 (2-18) d N 3 / d t = λ 2 N 2 (2-19) (17-2) (18-2). (19-2). N 1 λ 1.N 3 (19-2) (18-2) (17-2) : t N 1 = N 10 e λ 1 t N 2 = { λ 1 / (λ 2 λ 1 ) } N 10 ( e - λ 1 t e λ 2 t ) (2-20) N 3 = N 10 [1+ {λ 1 / (λ 2 λ 1 )}] e -λ2 t - {λ 2 / (λ 2 λ 1 )} e -λ1t ] (2-21). N 20 = N 30 = 0 N 30 N 20 : N 2 = { λ 1 / (λ 2 λ 1 ) } N 10 ( e -λ1t - e -λ2 t ) + N 20 e -λ2 t (2-22) N 3 = N 30 + N 20 ( 1- e -λ2 t ) + N 10 [ 1 + { λ 1 / (λ 2 λ 1 ) } e -λ2 t - { λ 2 / (λ 2 λ 1 ) } e -λ1t ] (2-23) 2

31 N 3 N 2 N 1 (9-2) Ru β - β - t 1/2 = 4.5 h Rh t 1/2 = 35 h Pd 100 N t (9-2) t N 3 N 2 N N 10 =100 N 20 = N 30 = 0. N 1 3

32 t = 0 N 2. (20-2). N 3 (%100 ).( 5 ) Radioactive equilibrium : N 3 N 2 N 1 d N 1 / dt = d N 2 / d t = dn 3 / d t (2-24) : d N 1 / d t = - λ 1 N 1 = 0 (2-25) d N 2 / d t = 0 = λ 1 N 1 λ 2 N 2 λ 1 N 1 = λ λ 2 N 2 (2-26).( N 1 ) λ λ 1 = 0. The secular equilibrium. ) λ 1 4

33 .λ 1 < λ 2 (. (20-2) λ 1 : N 2 (λ 1 / λ 2 ) N 10 ( 1 e λ2 t ) λ 2 N 2 = λ 1 N 10 ( 1- e - λ2 t ) (2-27) e - λ 2t t (27-2) : λ 2 N 2 = λ 1 N 10 (2-28) (10-2). a.( ) λ 1 N 10 ( b ) c.λ 1 N 1. log a 2 a c 1 b t 5

34 :(10-2) λ 1.(28-2) λ 2 ( ).λ : x : : λ 1 N 1 = λ 2 N 2 : N 1 / N 2 = λ 2 / λ 1 = t 1 / t 2 : 2.8 x 10 6 x 1620 = 1 x t 1 : t 1 = 4.54 x 10 9 years The transient equilibrium 6

35 .(transient equilibrium) ) λ 2 λ 1 ) λ 1 ( λ 2 > λ 1 λ 1.( e - λ 2t.= 0. e - λ 1t : (20-2) N 2 = { λ 1 / (λ 2 λ 1 )} N 10 e -λ1t = { λ 1 / (λ 2 λ 1 )} N 1 (2-29). A : A 1 / A 2 = λ 1 N 1 / λ 2 N 2 = (λ 2 λ 1 ) / λ 2 (2-30). (11-2) t = 0 t. log A 2 a c 1 b 7

36 2 4 6 t :(11-2) The natural radioactive series ( ) 232 Th x2.2 9 (1-2). 10x3. :(1-2)

37 Sm 19 K. 9.( 10 ) ( ) The induced radioactivity Co + n 27 Co + γγ (neutron radioactive capture) : Co Ni + β - + ν 9

38 ..(Trans- uranium elements) : U + 1 0n U + γ U Np + β - + ν Np Pu + β - + ν. ) 95Am. ( ) 96Cm ( 98Cf ( ) 97Bk ( ) 100Fm 99Es... 0

39 P d P + p ) ( : N + He F + n α U + O Fm + 4 n ( ) (cross-section) 1

40 (barn) : ( 10 = 1 ) : (18-2) dn 2 /d t = λλ 1 N 1 λλ 2 N 2 λλ 1 N 1. λλ 2 N 2 N. λλ 1 N 1 ) n N 10 σ ( : vν λ 1 N 1 = N = n v νσ N 10 (2-31) : λλ 1 N 1 dn 2 / d t = n v σ N 10 λ 2 N 2 (2-32) : N 2 N 2 = [ n v σ N 10 / λ ] ( 1- e -λλ2t ) (2-33) 2

41 . : t 1/2 ( 1- e - λ2t ) λ 2 t N 2 = n v σνn 10 t : (33-2) ( ) : ( 1- e - λ2t ) = 1 : (33-2) N 2 = n v σ N 10 / λ 2 (2-35)... ) n N 10.( Units of radioactivity 9-2 (µµ Ci) (mci) Courie (Ci) ).226 ( : x = 1Ci

42 4 10 x3.7 = 10 x3.7 = 7 1mCi 1µµCi ( )... (Becquerel). : 1 = 3 10 = 6 10 = 9 10 = = 1Bq 1 K Bq 1 M Bq 1 G Bq 1 T Bq 6 10 Rutherford (rd). : Ra, Ra, Ac, U, Th

43 ββ Ag, Cu, Co, Na Po, Am, Bi, Ra Cs(β - ), Sr(β - ), K(β +,β - ), 22 11Na(β + ) : ( )

44 : Nd Pm Sm : Th U Pa 89 Ac

45 / M 3 M 2 L 3 L 2 K

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