6. [1] (cal) (J) (kwh) ( ( 3 t N(t) dt dn ( ) dn N dt N 0 = λ dt (3.1) N(t) = N 0 e λt (3.2) λ (decay constant), λ [λ] = 1/s
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1 filename=decay-text tex made by R.Okamoto, Emeritus Prof., Kyushu Inst.Tech. * 1, radioactive ray ( parent nucleus) ( daughter nucleus) disintegration, decay ( 4 He) X 5., 1
2 6. [1] (cal) (J) (kwh) ( ( 3 t N(t) dt dn ( ) dn N dt N 0 = λ dt (3.1) N(t) = N 0 e λt (3.2) λ (decay constant), λ [λ] = 1/s
3 N 0 N(t) = N 0 (1 e λt ) (3.3) (3.2) N 0 t N(t) (3.2) t e λt t t + dt p(t)dt t e λt t t + dt λdt p(t)dt = e λt λdt t 0 p(t)dt = 0 e λt λdt = 1 (3.4) 1 4 t dt dn dn/n 0 mean life τ τ 0 t ( 1) dn dt 1 dt = λ t e λt dt. (4.5) N 0 0 f(x), g(x) f (x)g(x)dx = f(x)g(x) f(x)g (x)dx 0 t e λt dt = t d [ ] [ ] 1 t 1 0 dt λ e λt dt = λ e λt λ e λt dt = 1 [ ] e λt λ = 1 (4.6) 2 0 λ 2 τ τ = 1 λ (4.7) τ λ (half life)(t, T 1/2 ) τ N(t + T ) = 1 2 N(t) T = ln 2 λ = = τ. (4.8) λ 3
4 5 Ci( ) Bq( ) ( ) Ci 1. Bq( ) (Bq) Bq Bq 1/s. (5.9) 1kBq = 10 3 Bq = 1000, 1MBq(1 ) = 10 6 Bq =, 1GBq(1 ) = 10 9 Bq = Ci( ) Ci g Ra Ci Bq Ci Ci Bq, (5.10) 1mCi 10 3 Ci, 1µCi 10 6 Ci, 1nCi 10 9 Ci, 1pCi Ci. (5.11) (t) (t) λn(t) (6.12) [2][3][4] (t) [(t)] = 1/s M T m N a (6.12). (t) = ln 2 T m M N a. (6.13) [2] 4
5 1. t N(t) N 0 e λt dn/dt = λn(t) 2., B, C, B N B (t) e λ Bt B B (t) λ B N B (t) 3. (6.12) 4. t = 0 1. R : dn(t) dt = R λn(t) (6.14) N 0 0 λn 0 N(t) = N 0 e λt + R λ (1 e λt ), (6.15) (t) λn(t) = 0 e λt + R(1 e λt ) (6.16) 2. R(t) dn(t) dt = R(t) λn(t), (6.17) N(t) = N 0 e λt + (t) λn(t) = 0 e λt + λ R(t) t 0 t R(t ) e λ(t t ) dt, (6.18) 0 R(t ) e λ(t t ) dt. (6.19) 5
6 6.2 a b c N a, N b, N c, λ a, λ b a N 0 dn a dt dn b dt dn c dt = λ a N a, = λ b N b + λ a N a, = λ b N b (6.20) N a (t) = N 0 e λat, (6.21) ) ( λa N b (t) = λ b λ a ( N c (t) = N 0 N 0 (e λ at e λ bt ), (6.22) 1 λ b λ b λ a e λat + λ ) a e λ bt λ b λ a (6.23), a (t) = λ a N a (t), b (t) = λ b N b (t), c (t) = λ c N c (t) 6.3 a b λ a, λ b λ eff λ eff = λ a + λ b, τ eff = dn = λ a Ndt λ b Ndt λ eff Ndt (6.24) 1 τ eff = 1 τ a + 1 τ b, 1 T eff = 1 T a + 1 T b, (6.25) τ a τ b τ a + τ b, T eff = T at b T a + T b (6.26) τ a, τ b, τ eff (T a, T b, T eff ) a,b (t) λ eff N(t) = λ eff N 0 e λ efft 6
7 7 specific radioactivity S m S m (7.27) S Bq/g Bq/Kg SI N M N N = N /M, = λn (7.27) S = λn M (7.28) T 1/2 (y, year) (s, second) S = Bq/g, S = Bq/g (7.29) (T 1/2 /y)(m/g) (T 1/2 /s)(m/g) 8 α 2 2 (a) Y ZX N 4 Z 2Y N 2 + α( 4 2He 2 ) + Q. (8.30) Q Q = (M X M Y M α )c 2, (8.31) M E α Y V y, V α Q = 1 2 M yv 2 y M αv 2 α (8.32) = 1 2 M αvα 2 (1 + M yvy 2 ). (8.33) M α Vα 2 7
8 M y V y = M α V α. (8.34) E α 1 2 M αv 2 α Q = E α (1 + M α M y ) M y E α = Q( ). (8.35) M α + M y (b) Y Y ZX N 4 Z 2YN 2 + α( 4 2He 2 ) + Q. (8.36) Q ( E y) Q = Q E y ( 1928 Gamov, Condon, Gurney r 2(Z 2)/(4πε 0 r) r R 2(Z 2)/(4πε 0 R) 8.6MeV 4.2MeV 9 β Z N M(, Z) M (, Z), Z B e M(, Z) = M (, Z) + Z m e + B e /c 2 (9.37) 8
9 B e M(, Z) = M (, Z) + Z m e (9.38) 1. β n p + e + ν (T = 1000s) (9.39) β n p + e + ν (9.40) 3 1H 3 2He + e + ν (T = 12y ), (9.41) 32 15P 32 16S + e + ν (T = 14d ) (9.42) ν anti-neutrino β ZX N Z+1 Y N 1 + e + ν + Q(β ). (9.43) β Q(β ) ZX N Z+1 Y N 1 + e + ν + Q (β ) (9.44) Q (β ) Q(β ) E ex (Q (β ) = Q(β ) E ex ) Q (β ) < Q(β ) Q(β ) [M (, Z) M (, Z + 1) m e ] c 2 > 0. (9.45) Q(β ) [M(, Z) M(, Z + 1)] c 2 > 0 (9.46) Q(β ) [m n m p ] c 2 = 0.5 MeV > 0 (9.47) 9
10 2. β + β + p n + e + + ν (9.48) 10 6 C 10 5 B + e + + ν (T = 19.4s ), (9.49) 11 6 C 11 5 B + e + + ν (T = 20.3min ) (9.50) e + e 0.5 MeV γ 2 ( ) β +, ZX N Z 1 Y N+1 + e + + ν + Q(β + ). (9.51) β + ZX N Z 1 Y N+1 + e + + ν + Q (β + ) (9.52) Q (β + ) Q Q (β + ) < Q(β + ) β Q(β + ) Q(β + ) [M (, Z) M (, Z 1) m e ] c 2 > 0 (9.53) Q(β + ) [M(, Z) M(, Z + 1) 2m e ] c 2 > 0 (9.54) 3. electron capture, EC : p + e n + ν (9.55) 10
11 7 4Be + e 7 3Li + ν (T = 53.6d) (9.56) ZX N e Z 1 Y N+1 + ν + Q. (9.57) Q(EC) [M (, Z) + m e M (, Z 1)] c 2 I > 0 (9.58) I (ionization energy) Q(EC) [M(, Z) M(, Z 1)] c 2 I > 0 (9.59) I ev Q(EC) 10eV K K (K ) K K X uger process uger electron 4. β 5. β β BE(, Z) = c v c s 2/3 c a (N Z) 2 Z 2 c c + δ(, Z), (9.60) 1/3 c v = MeV, c s = MeV, c a = MeV, c c = MeV, (9.61) 11
12 11.2 MeV (Z, ) 1/2 δ(z, ) = 0 ( ) 11.2 MeV (Z, ) 1/2 (9.62), Z M(, Z)c 2 = [M H Z + ( Z)m n ] c 2 BE(, Z) = [M H Z + ( Z)m n ] c 2 c v + c s 2/3 [(/2) Z] 2 + c a Z 2 +c c δ(, Z). (9.63) 1/3 M(, Z) M H m n [?]) Z 2 Z β 0 = M(, Z) Z = (M H m n )c 2 4c a + 8c a Z + 2c c 1/3 Z Z β = 2c a + (m n M H )c 2 (9.64) 4c a + c c 2/ ( c (9.65) c 2c a ) 2/3 Z β = /3 (9.66) /3 (9.67) N(= Z) Z β Heisenberg, β (Heisenberg ) = 63 Z β 28.15, = 135 Z β γ 12
13 gamma decay X X X + γ (10.68) E i, E f, λ, ν E i E f hν(= h hc ). (10.69) ω P ( recoil) E i = E f + P 2 P hν c 2M + hν, (10.70) = 0, (10.71) E i E f = ( hν c )2 + hν (10.72) 2M MeV 940MeV R.Meyer s metastable state isomeric transition 103 Rh 103 Rh m 57 [1] 1983 pp.6 9 [2] 1998 p.60 p.62 (3-101) t T t ( 13
14 [3] J. R. ( ) 1995 p 13, pp [4] J. R. ( ) 2003 pp
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23 1 Section ( ) ( ) ( 46 ) , 238( 235,238 U) 232( 232 Th) 40( 40 K, % ) (Rn) (Ra). 7( 7 Be) 14( 14 C) 22( 22 Na) (1 ) (2 ) 1 µ 2 4
23 1 Section 1.1 1 ( ) ( ) ( 46 ) 2 3 235, 238( 235,238 U) 232( 232 Th) 40( 40 K, 0.0118% ) (Rn) (Ra). 7( 7 Be) 14( 14 C) 22( 22 Na) (1 ) (2 ) 1 µ 2 4 2 ( )2 4( 4 He) 12 3 16 12 56( 56 Fe) 4 56( 56 Ni)
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56 4 2 log N ( t ) 1 0 0 t 1/2 τ m 2τ m time t 4.1: λ decay rate λ = 1 τ m (4.8) A B b Γ = h τ m = hλ (4.9) A B + b (4.10) Q Q = M(B)+M(b) M(A) (4.11)
4 4.1 t N(t) t t +dt dn(t) N(t) dn(t) = λn(t)dt (4.1) dn(t) dt = λn(t) (4.2) t =0 N 0 = N(0) 4.1 N(t) =N 0 e λt (4.3) log N(t) = log N 0 λt (4.4) mean life half-life t N(t) τ m =1/λ 1/e τ m 1/2 t 1/2 T
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m d y dt = F m d y = mg dt V y = dy dt d y dt = d dy dt dt = dv y dt dv y dt = g dv y dt = g dt dt dv y = g dt V y ( t) = gt + C V y ( ) = V y ( ) = C = V y t ( ) = gt V y ( t) = dy dt = gt dy = g t dt
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第89回日本感染症学会学術講演会後抄録（I）
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hirameki_09.dvi
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W 1983 W ± Z cm 10 cm 50 MeV TAC - ADC ADC [ (µs)] = [] (2.08 ± 0.36) 10 6 s 3 χ µ + µ 8 = (1.20 ± 0.1) 10 5 (Ge
![W 1983 W ± Z cm 10 cm 50 MeV TAC - ADC ADC [ (µs)] = [] (2.08 ± 0.36) 10 6 s 3 χ µ + µ 8 = (1.20 ± 0.1) 10 5 (Ge](/thumbs/91/105929864.jpg "W 1983 W ± Z cm 10 cm 50 MeV TAC - ADC ADC [ (µs)] = [] (2.08 ± 0.36) 10 6 s 3 χ µ + µ 8 = (1.20 ± 0.1) 10 5 (Ge")
22 2 24 W 1983 W ± Z 0 3 10 cm 10 cm 50 MeV TAC - ADC 65000 18 ADC [ (µs)] = 0.0207[] 0.0151 (2.08 ± 0.36) 10 6 s 3 χ 2 2 1 20 µ + µ 8 = (1.20 ± 0.1) 10 5 (GeV) 2 G µ ( hc) 3 1 1 7 1.1.............................
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日本糖尿病学会誌第58巻第1号
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