{VERSION 4 0 "IBM INTEL NT" "4.0" } {USTYLETAB {CSTYLE "Maple Input" -1 0 "Courier" 0 1 255 0 0 1 0 1 0 0 1 0 0 0 0 1 }{CSTYLE "2D Math" -1 2 "Times" 0 1 0 0 0 0 0 0 2 0 0 0 0 0 0 1 }{CSTYLE "Hyperlink" -1 17 "" 0 1 0 128 128 1 2 0 1 0 0 0 0 0 0 1 }{CSTYLE "2D Comment" 2 18 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 } {CSTYLE "" -1 256 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 257 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 258 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 259 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 260 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 } {CSTYLE "" -1 261 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 262 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 263 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 }{PSTYLE "Normal" -1 0 1 {CSTYLE "" -1 -1 "Tim es" 1 12 0 0 0 1 2 2 2 2 2 2 1 1 1 1 }1 1 0 0 0 0 1 0 1 0 2 2 0 1 } {PSTYLE "Heading 1" -1 3 1 {CSTYLE "" -1 -1 "Times" 1 18 0 0 0 1 2 1 2 2 2 2 1 1 1 1 }1 1 0 0 8 4 1 0 1 0 2 2 0 1 }{PSTYLE "Heading 3" -1 5 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 1 1 2 2 2 2 1 1 1 1 }1 1 0 0 0 0 1 0 1 0 2 2 0 1 }{PSTYLE "Title" -1 18 1 {CSTYLE "" -1 -1 "Times " 1 18 0 0 0 1 2 1 1 2 2 2 1 1 1 1 }3 1 0 0 12 12 1 0 1 0 2 2 19 1 } {PSTYLE "Normal" -1 256 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 1 1 1 }3 1 0 0 0 0 1 0 1 0 2 2 0 1 }} {SECT 0 {EXCHG {PARA 18 "" 0 "" {TEXT -1 26 "Radioaktiivinen hajoamine n" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 101 "Rad ioaktiivinen hajoaminen on ilmi\366, jossa aktivoitunut, ep\344stabiil i atomiydin vapauttaa energiaansa " }{XPPEDIT 18 0 "alpha;" "6#%&alpha G" }{TEXT -1 3 "-, " }{XPPEDIT 18 0 "beta;" "6#%%betaG" }{TEXT -1 6 "- tai " }{XPPEDIT 18 0 "gamma;" "6#%&gammaG" }{TEXT -1 38 "-s\344teilyn kautta. Hiukkass\344teilyn eli " }{XPPEDIT 18 0 "alpha;" "6#%&alphaG " }{TEXT -1 5 "- ja " }{XPPEDIT 18 0 "beta;" "6#%%betaG" }{TEXT -1 538 "-s\344teilyn tapauksessa samalla muuttuu my\366s atomiytimen sis \344inen kokoonpano. T\344llaisen hajoamisen kautta alkuaine muuttuu t oiseksi. \n\nErityisen paljon tutkittuja ovat ydinreaktorien polttoain esauvoihin j\344\344vien radioaktiivisten aineiden hajoamisketjut. Pol ttoainesauvoista muodostuva pitk\344\344n radioaktiivinen j\344te aihe uttaa huolestumista, koska sauvoissa olevien radioaktiivisten aineiden hajoaminen on niin hidasta, ett\344 s\344teilyongelma s\344ilyy luonn ollisen hajoamisen kautta akuuttina vuosituhansia. T\344ss\344 esimerk iss\344 tarkastelemme radiumin " }{BITMAP 40 17 17 1 "?TMOX:B:nH>?:]:= J\\:B:jyyyyK:VquXQKF\\KNquXqK::::::::?cB?CJ?cB;d:?cB^[F\\K^@>:ZK>^;N\\;>^Lb>_:;:R>B:D;B:;:R>ZMN^LJ:<:ZK:@jBD;;B::@K S@LCJ:D[:B::@kB^@DLKD;<:ZK>>aBJ@kB;C:]Z:>:@:=R>_RB]BG @KJDjB<<;:ab>;r>_b>DKK@KS@<>:FZZR:HK[DkBR>;K:<:FZnR:cS:]CB>::DJZDK;^LF:_jJ<<;:Z;N`LFZljR<<;::]J:@;_5:" }{TEXT -1 43 " hajoamis ta sek\344 yksinkertaistettua radium " }{BITMAP 40 17 17 1 "?TMOX:B:nH >?:]:=J\\:B:jyyyyK:VquXQKF\\KNquXqK::::::::?cB?CJ?cB;d:?cB^[F\\K^@>:ZK>^;N\\;>^Lb>_:;:R>B:D;B:;:R>ZMN^LJ:<:ZK:@jBD; ;B::@KS@LCJ:D[:B::@kB^@DLKD;<:ZK>>aBJ@kB^:F\\ZB:;Z ;j:@KC:V\\L>ZMN<=BB?S>_SB:FZZ>Z;bB=CG]R>]R>;K:<:FZnR:c S>D;<:Z<>bLNZ:O\\KF^ZJ::R:;c>=JCF`ZJ::R:_c>=bF:;::]ZK:1:" }{TEXT -1 32 " ytimen hajoamisketjua lyijyksi " }{BITMAP 40 16 16 1 "?TMgW:B: nH>?:[Z:F:C:;::JB;:jB@k B<<;r>]BGB::@KJB:@[M>B<:ZKB:B:D;B::@KSD;C:]ZLF\\ZR:]b>=S>cSB]BG;R>;kBb>;B:>ZK>^>?b>b LN<_b:aBJ::@JSDkCDLC@jR>:;::]j:@KJN<1:" }{TEXT -1 50 ". T\344m\344 ketju muodostaa loppuosan varsin t\344rke\344st\344 \+ " }{BITMAP 39 16 16 1 "?TMOX:B:nH>?:]:=J\\:B:jyyyyK:VquXQKF\\KNq uXqK::::::::DLKDLZNZ\\>b\\>B;B::@kB@KJFZK>^K>>;B::F\\ZJ:D[LB:<::]:;b>D [:B::F<>ZLb>;d>B::CkB;B:@ZLF^K^`;F\\LV\\:G\\ZF^Z>:B:ab>N]bF]ZZZ:B:=BB;Z<>bLR>DJZB:<:Z;>^LNZ;?^;J:B::@JSDk:@ MJ@JS>Z:B::F\\Z>ZLjB3:" }{TEXT -1 313 " hajoamisketjusta. \n\nJokaisel le radioaktiiviselle atomiytimelle on olemassa tietty todenn\344k\366i syys sen hajoamiseen m\344\344r\344tyll\344 aikav\344lill\344. Hajoami sen kautta syntyvien tyt\344ratomien lukum\344\344r\344 on siten suora an verrannollinen aktiivisten atomiytimien lukum\344\344r\344\344n. Ni inp\344 voidaan m\344\344ritt\344\344 radioaktiivinen hajoamislaki " } }{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 256 "" 0 "" {XPPEDIT 18 0 "diff (N,t) = -lambda*N;" "6#/-%%diffG6$%\"NG%\"tG,$*&%'lambdaG\"\"\"F'F,!\" \"" }{TEXT -1 1 "," }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 6 "miss\344 " }{TEXT 256 1 "N" }{TEXT -1 40 " on radioaktiivi sten ytimien lukum\344\344r\344, " }{TEXT 257 1 "t" }{TEXT -1 12 " on \+ aika ja " }{XPPEDIT 18 0 "lambda;" "6#%'lambdaG" }{TEXT -1 190 " radio aktiivinen hajoamisvakio, joka m\344\344ritt\344\344 todenn\344k\366is yyden atomiytimen spontaanille hajoamiselle annetulla ajanhetkell\344. Hajoamislain perusteella voidaan m\344\344ritt\344\344 ns. puoliintum isaika " }{BITMAP 27 19 19 1 "?TMGW:B:nH>?V=V::DLLV\\:cB?CJ>:R>_j:<\\KF\\ZB:;:@JJF :F`ZB:?KK<^;>>=Z:NZ;j:BC=BB=BB;[Lr>=CB>Z;Z;>>D[;N<;ZLB:<:CC:]BB?BJ::_:J::V <]BG=BG ?NDv>F:C:;::JBZ:::::::V\\:c >B:::::::=BGD;<::::::ZLNZLZ:::::::r>=DB>:::::::@jR<<;:::::::]BB>:::C;; ::::=BB>:::_B:>::::F^ZJ:::N<>::::N<>::bBCkC<^\\N^:K::::_:;::@KC:JKN^:S:F:F@:jBF\\ZR:;;><:ZK^@;R:F:< jC<^:>Z<^:>:::Z;N\\:>Z;>>=Z^FZZB:;R:]R>]ZZJ::::@JCRB;k:L]LFZZB: ;:::::@JCR>;[Lr>=CB>:::::R:aBJ@JJb>@JCB:;b:N><>;R:]R>]::<:CC:]BB?BJ>ZL B:<:@:]ZZJ::::_jB@[LZ:::::::::::b:b:B:::::R:^:B:::::JCF ZZF:;J:@JT@JJB:::::JCj:>:;jC@><:::::N:;:::::N:HKZ=CB>:@;<:::::N<]RB_:;bB;T>;[::::::_J:>:R>@LJ B:::::JCJ:ZKR>;C:<:::::N<>:r>?c>B:::::b:_:;:@jBJ:::::Z;N\\:J:::1:" } {TEXT -1 30 ". T\344ll\366in hajoamislaille p\344tee" }}{PARA 0 "" 0 " " {TEXT -1 0 "" }}{PARA 256 "" 0 "" {BITMAP 120 45 45 1 "?TM?r?> If?F:C:;::JB:::::::::b:?CJ=BGN^\\>b:B::::::::Z;F\\Zb>F\\K>>;B:::::::: :_ZLj:@MJB::Z\\^>DJLB:;::::?bB?CCNB::J;@kC<^[N<>::::FZKF\\LJC:;r >;L:<::FZZFZnr>aBJ>::::R:aBJN@jJ<\\:>::::jB<\\^:>Z:::::F<@JC>aRB;K:<::FZnR:;S:;T:cS:cK:Z:::ZKN`[N\\\\V\\:C:;::::?BJ=b>L<<::::]b >_R>]BB>::::F:=b>D;<::::N<_J:>::::F::<::::NbM>B<:::Z::::r>?S>_S>;[::::R:_SB;[:::::R>]R>]JJB::DLK<^^>:?BC;J::;B:::DLKDLK^>>::::Z;^@=r>^:B:::::NZ\\N^\\JZ>Z::::_jJ@KJB:::::FZKF\\KJJB:::JCF\\K>>CK:>::]ZK::<;aBJ]RBc;;:::@;]JCJ:::::FZ\\F\\ZN<;J:::::::::j:@ lBN<>:::::::::F:_JCJ:::::::::j:@MCZ:>:::::::::N^KN\\^;F\\L>Z:bBC[aZ;F<@LJ:;r>D;<::=ZMB:=ZKN\\:J: :::R:N<_J:>Z;^`LZ::j:<\\;:?R>_B:>::::@Z:N<_J:>Z;N\\:J::j:LM:@JJFZZFZKN <>::::@Z:N<_J:>:aZ:>::r>@:Lm:DkC<>;:::Z;jCN<>:=BG;B:<::@KSB:DkJDk:]b>=:;:::Z;>^;N\\K>^:B:?BC=J:>Z:::N\\ :b>]BB=BB;J::::R:B:j:DK;D;;B:::_B:HkBZ::Z<>b< B:?RB]BB?s>B::::@JJB:j:DmJ::R:j:@;]Z:>Z::::RB;[::@[:>:;::F;[::::5:" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 3 "" 0 "" {TEXT -1 30 "Yksinkertainen hajoamistilanne" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }} {PARA 0 "" 0 "" {TEXT -1 7 "Radium " }{BITMAP 40 17 17 1 "?TMOX:B:nH>? :]:=J\\:B:jyyyyK:VquXQKF\\KNquXqK::::::::?cB?CJ?cB;d:?cB^[F\\K^@>:ZK>^;N\\;>^Lb>_:;:R>B:D;B:;:R>ZMN^LJ:<:ZK:@jBD;;B: :@KS@LCJ:D[:B::@kB^@DLKD;<:ZK>>aBJ@kB;C:]Z:>:@:=R>_RB ]BG@KJDjB<<;:ab>;r>_b>DKK@KS@<>:FZZR:HK[DkBR>;K:<:FZnR:cS:]CB>::DJZDK; ^LF:_jJ<<;:Z;N`LFZljR<<;::]J:@;_5:" }{TEXT -1 34 " on yk si v\344liydin pitk\344aktiivisen " }{BITMAP 39 16 16 1 "?TMOX:B:nH>?: ]:=J\\:B:jyyyyK:VquXQKF\\KNquXqK::::::::DLKDLZNZ\\>b\\>B;B::@kB@ KJFZK>^K>>;B::F\\ZJ:D[LB:<::]:;b>D[:B::F<>ZLb>;d> B::CkB;B:@ZLF^K^`;F\\LV\\:G \\ZF^Z>:B:ab>N]bF]ZZZ:B:=BB;Z< >bLR>DJZB:<:Z;>^LNZ;?^;J:B::@JSDk:@MJ@JS>Z:B::F\\Z>ZLjB3:" }{TEXT -1 21 ":n hajoamisketjussa. " }{BITMAP 40 17 17 1 "?TMOX:B:nH>?:]:=J\\:B:jyyyyK:VquXQKF\\KNquXqK::::::::?cB?CJ?cB;d:?cB ^[F\\K^@>:ZK>^;N\\;>^Lb>_:;:R>B:D;B:;:R>ZMN^LJ:<:ZK:@jBD;;B::@KS@LCJ:D [:B::@kB^@DLKD;<:ZK>>aBJ@kB;C:]Z:>:@:=R>_RB]BG@KJDjB< <;:ab>;r>_b>DKK@KS@<>:FZZR:HK[DkBR>;K:<:FZnR:cS:]CB>::DJZDK;^LF:_jJ<<;:Z;N`LFZljR<<;::]J:@;_5:" }{TEXT -1 67 ":n puoliintumisa ika on 5,75 vuotta kun se hajoaa lyhytaktiiviseksi " }{BITMAP 39 17 17 1 "?TMOX:B:nH>?v>Fb b:N^^Z::F\\K>^;F\\K>^B<:ZM>b_ZLJ:<::@JT@LCb>>Z::Z;N\\KNDLKN^\\JLjC@K JB:R>]jB@KK@kCj:DK:=BG=CBF:>Z::aBJH[MN<>: :Ll:?:]:=J\\:B:jyyyyK:VquXQKF\\KNquXqK::::::::?cB?CJ?cB;d:?cB< Z::F\\KF\\\\F\\K>^[F\\K^@>:ZK>^;N\\;>^Lb>_:;:R>B:D;B:;:R>ZMN^LJ:<:ZK:@ jBD;;B::@KS@LCJ:D[:B::@kB^@DLKD;<:ZK>>aBJ@kB;C:]Z:>:@ :=R>_RB]BG@KJDjB<<;:ab>;r>_b>DKK@KS@<>:FZZR:HK[DkBR>;K:<:FZnR:cS:]CB>: :DJZDK;^LF:_jJ<<;:Z;N`LFZljR<<;::]J:@;_5:" }{TEXT -1 127 ":sta on j\344ljell\344 70 vuoden kuluttua. \n\nLaskujen aluksi on syyt\344 h\344vitt\344\344 mahdollisista aiemmista laskuista j\344 \344neet muuttujat. \n" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "re start;" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 48 "Ytimien hajoamista kuvaava differentiaaliyht\344l\366." } }{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 33 "yht:= diff(n(t), t)=-lambda*n(t);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 43 "Alkuehdon m\344\344ritt \344\344 tilanne, jossa on vain " }{BITMAP 40 17 17 1 "?TMOX:B:nH>?:]: =J\\:B:jyyyyK:VquXQKF\\KNquXqK::::::::?cB?CJ?cB;d:?cB^[F\\K^@>:ZK>^;N\\;>^Lb>_:;:R>B:D;B:;:R>ZMN^LJ:<:ZK:@jBD;;B::@K S@LCJ:D[:B::@kB^@DLKD;<:ZK>>aBJ@kB;C:]Z:>:@:=R>_RB]BG @KJDjB<<;:ab>;r>_b>DKK@KS@<>:FZZR:HK[DkBR>;K:<:FZnR:cS:]CB>::DJZDK;^LF:_jJ<<;:Z;N`LFZljR<<;::]J:@;_5:" }{TEXT -1 52 " ytimi \344. Lasketaan ainem\344\344r\344 suoraan kilogrammoissa." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "alk uehto:= n(0)=100;" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 " " 0 "" {TEXT -1 33 "Ratkaistaan differentiaaliyht\344l\366." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 36 "r tk:= dsolve(\{yht, alkuehto\}, n(t));" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 58 "Sijoitetaan hajoamisvakio . K\344ytet\344\344n aikayksikk\366n\344 vuosia." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 47 "ainemaara:= subs(lambda=log(2)/5.75, rhs(rtk));" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 80 "Piirret\344\344n kuvaaja ainem \344\344r\344n kehitykselle ajan fuktiona 50 vuoden aikajaksolla." }} {PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "plot(ainemaara, t=0..50);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 106 "70 vuoden j\344lkeen j\344ljelle j \344\344neen ainem\344\344r\344n paino kilogrammoissa selvi\344\344 si joittamalla ajaksi 70 vuotta." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 43 "jaljella:= subs(t=70, ainema ara):\nevalf(%);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 " " 0 "" {TEXT -1 38 "Tuloksena on siis 21,6 grammaa Radium " }{BITMAP 40 17 17 1 "?TMOX:B:nH>?:]:=J\\:B:jyyyyK:VquXQKF\\KNquXqK::::::: :?cB?CJ?cB;d:?cB^[F\\K^@>:ZK>^;N\\;>^Lb>_:;:R>B:D;B: ;:R>ZMN^LJ:<:ZK:@jBD;;B::@KS@LCJ:D[:B::@kB^@DLKD;<:ZK>>aBJ@kB;C:]Z:>:@:=R>_RB]BG@KJDjB<<;:ab>;r>_b>DKK@KS@<>:FZZR:HK[DkBR>; K:<:FZnR:cS:]CB>::DJZDK;^LF:_jJ<<;:Z;N`LFZljR<<;::]J:@;_ 5:" }{TEXT -1 6 ":aa. \n" }}{PARA 3 "" 0 "" {TEXT -1 13 "Hajoamisketju " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 12 "My \366s Radium " }{BITMAP 40 17 17 1 "?TMOX:B:nH>?:]:=J\\:B:jyyyyK :VquXQKF\\KNquXqK::::::::?cB?CJ?cB;d:?cB^[F\\K^@>:ZK >^;N\\;>^Lb>_:;:R>B:D;B:;:R>ZMN^LJ:<:ZK:@jBD;;B::@KS@LCJ:D[:B::@kB^@DL KD;<:ZK>>aBJ@kB^:F\\ZB:;Z;j:@KC:V\\L>Z MN<=BB?S>_SB:FZZ>Z;bB=CG]R>]R>;K:<:FZnR:cS>D;<:Z<>bLNZ:O\\KF^ZJ::R :;c>=JCF`ZJ::R:_c>=bF:;::]ZK:1:" }{TEXT -1 13 " on v\344liydin " } {BITMAP 39 16 16 1 "?TMOX:B:nH>?:]:=J\\:B:jyyyyK:VquXQKF\\KNquXq K::::::::DLKDLZNZ\\>b\\>B;B::@kB@KJFZK>^K>>;B::F\\ZJ:D[LB:<::]:;b>D[:B ::F<>ZLb>;d>B::CkB;B:@ZLF^K^`;F\\LV\\:G\\ZF^Z>:B:ab>N]bF]ZZZ:B:=BB;Z<>bLR>DJZB:<:Z;>^LNZ;?^;J:B::@JSDk:@MJ@ JS>Z:B::F\\Z>ZLjB3:" }{TEXT -1 35 ":n hajoamisketjussa. Hajoamisketju \+ " }{BITMAP 40 17 17 1 "?TMOX:B:nH>?:]:=J\\:B:jyyyyK:VquXQKF\\KNq uXqK::::::::?cB?CJ?cB;d:?cB^[F\\K^@>:ZK>^;N\\;>^Lb>_ :;:R>B:D;B:;:R>ZMN^LJ:<:ZK:@jBD;;B::@KS@LCJ:D[:B::@kB^@DLKD;<:ZK>>aBJ@ kB^:F\\ZB:;Z;j:@KC:V\\L>ZMN<=BB?S>_SB< J:>:FZZ>Z;bB=CG]R>]R>;K:<:FZnR:cS>D;<:Z<>bLNZ:O\\KF^ZJ::R:;c>=JCF`ZJ:: R:_c>=bF:;::]ZK:1:" }{TEXT -1 129 " ytimest\344 eteenp\344in sis \344lt\344\344 useita lyhytaikaisia ja muutamia pitk\344aikaisia v\344 liytimi\344 ennen hajoamista pysyv\344ksi lyijy-ytimeksi " }{BITMAP 40 16 16 1 "?TMgW:B:nH>?:[Z:F:C:;::JB;:jB@kB<<;r>]BGB::@KJB:@[M>B<:ZKB:B:D;B::@KSD ;C:]ZLF\\ZR:]b>=S>cSB ]BG;R>;kBb>;B:>ZK>^>?b>bLN<_b:aBJ::@JSDkCDLC@jR>:;::]j :@KJN<1:" }{TEXT -1 42 ". Tarkastelemme nyt hajoamista v\344liytimet \+ " }{BITMAP 40 17 17 1 "?TMOX:B:nH>?:]:=J\\:B:jyyyyK:VquXQKF\\KNq uXqK::::::::?cB?CJ>Z^N^:K::F\\KF\\ZJ:HkBL=<:ZK>>;\\::R>@JJB: :@;b[>><:ZK>^;V\\:S>_c>B::@KJ]BBDJKLL;DL ZDJK>ZK>>]ZL>Z:R:]b>=R>;S:]J:@KJDjB<;b>V_SB_J:D;;B:=BBj:F\\K R>;C:?b>>Z:FZnb>F:;J:DJZD[Lb:;\\:B::@JJDK;D[;J:B::@JSDk:D[;N@; B:<::]J:D;]5:" }{TEXT -1 4 " ja " }{XPPEDIT 18 0 "Bi^212;" "6#*$%#BiG \"$7#" }{TEXT -1 66 " huomioiden. 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ZMW`M?`=V`:V@[[Okd::::Z:ZO;jbDkBDkDPodP?:::ZKgdmVD[L:H]mB:>DZMsNHoS@kdP_O;:::@oDP_O;:::::::Z:ZO;ZL:e<:::R?f D::@kdRO:::::B:RO:R>@odRO:::jbP?e<:ZKG^Ojd:::::B:RO:R?@odfdO;:::eZO;:Z KGP_O;:ZKG^LN\\KfE[O;::FdKfdK[O;::::<:P?::]TOfD::]T>_b>jd:::P; RO::::Z:ZO;:ZOjd::NdLF\\KfdOSO:::jbP?e<::::<:P?::@?P?:jB@kdRO::::P;e<: :::<:P?::@?P?:jDRO::::RNRO::::B:RO::jDRO:::::::fdOgd?>dOgD[L:Pj< d:fd:ROdOgd?>DeTOe<:Z:ZO;::rFZ?JbPJ:dJS;ZoRG Z:V`o>:aC:RO::BNPjdPjdPo<<_?f:[DNPZJk<:ekdP_O;:ZJ?ZOgd?RO;B:;ROEB:Zo>ZoB :[k;DP_O;::::ZKsF@[K:jdRO::J :P_?fdOgDf:P?ZJ[O;::::jc>Zo>ZoR;aSGaSG;jS@Z?J:PmSfDP?:::::::::::: HmTHmT::Z:3:" }{TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 61 "Muodostetaan hajoamisketjua kuvaavat differenti aaliyht\344l\366t: \n" }}{PARA 256 "" 0 "" {XPPEDIT 18 0 "diff(N[1],t) = -lambda[1]*N[1];" "6#/-%%diffG6$&%\"NG6#\"\"\"%\"tG,$*&&%'lambdaG6# F*F*&F(6#F*F*!\"\"" }{TEXT -1 0 "" }}{PARA 256 "" 0 "" {XPPEDIT 18 0 " diff(N[2],t) = lambda[1]*N[1]-lambda[2]*N[2];" "6#/-%%diffG6$&%\"NG6# \"\"#%\"tG,&*&&%'lambdaG6#\"\"\"F1&F(6#F1F1F1*&&F/6#F*F1&F(6#F*F1!\"\" " }{TEXT -1 0 "" }}{PARA 256 "" 0 "" {XPPEDIT 18 0 "diff(N[3],t) = lam bda[2]*N[2]-lambda[3]*N[3];" "6#/-%%diffG6$&%\"NG6#\"\"$%\"tG,&*&&%'la mbdaG6#\"\"#\"\"\"&F(6#F1F2F2*&&F/6#F*F2&F(6#F*F2!\"\"" }{TEXT -1 0 " " }}{PARA 256 "" 0 "" {XPPEDIT 18 0 "diff(N[4],t) = lambda[3]*N[3];" " 6#/-%%diffG6$&%\"NG6#\"\"%%\"tG*&&%'lambdaG6#\"\"$\"\"\"&F(6#F0F1" } {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 6 "jossa " }{XPPEDIT 18 0 "N[1];" "6#&%\"NG6#\"\"\"" }{TEXT -1 4 " \+ on " }{BITMAP 40 17 17 1 "?TMOX:B:nH>?:]:=J\\:B:jyyyyK:VquXQKF\\ KNquXqK::::::::?cB?CJ?cB;d:?cB^[F\\K^@>:ZK>^;N\\;>^L b>_:;:R>B:D;B:;:R>ZMN^LJ:<:ZK:@jBD;;B::@KS@LCJ:D[:B::@kB^@DLKD;<:ZK>>a BJ@kB^:F\\ZB:;Z;j:@KC:V\\L>ZMN<=BB?S>_ SB:FZZ>Z;bB=CG]R>]R>;K:<:FZnR:cS>D;<:Z<>bLNZ:O\\KF^ZJ::R:;c>=JCF`Z J::R:_c>=bF:;::]ZK:1:" }{TEXT -1 22 "-atomien lukum\344\344r\344 j a " }{XPPEDIT 18 0 "lambda[1];" "6#&%'lambdaG6#\"\"\"" }{TEXT -1 13 " \+ vastaavasti " }{BITMAP 39 16 16 1 "?TMOX:B:nH>?:]:=J\\:B:jyyyyK: VquXQKF\\KNquXqK::::::::?cB?CJ?cB;d:?cB^[F\\K^@>:ZK> ^;N\\;>^Lb>_:;:R>B:D;B:;:R>ZMN^LJ:<:ZK:@jBD;;B::@KS@LCJ:D[:B::@kB^@DLK D;<:ZK>>aBJ@kB^:F\\ZB:;Z;j:@KC:V\\L>ZM N<=BB?S>_SB:FZZ>Z;bB=CG]R>]R>;K:<:FZnR:cS>D;<:Z<>bLNZ:O\\KF^ZJ::R: ;c>=JCF`ZJ::R:_c>=bF:;::]ZK:1:" }{TEXT -1 42 ":n hajoamisvakio. Va staavasti alaindeksi '" }{TEXT 259 1 "2" }{TEXT -1 10 "' viittaa " } {BITMAP 40 17 17 1 "?TMOX:B:nH>?:]:=J\\:B:jyyyyK:VquXQKF\\KNquXq K::::::::?cB?CJ>Z^N^:K::F\\KF\\ZJ:HkBL=<:ZK>>;\\::R>@JJB::@; b[>><:ZK>^;V\\:S>_c>B::@KJ]BBDJKLL;DLZDJ K>ZK>>]ZL>Z:R:]b>=R>;S:]J:@KJDjB<;b>V_SB_J:D;;B:=BBj:F\\KR>; C:?b>>Z:FZnb>F:;J:DJZD[Lb:;\\:B::@JJDK;D[;J:B::@JSDk:D[;N@;B:< ::]J:D;]5:" }{TEXT -1 5 ":n, '" }{TEXT 260 1 "3" }{TEXT -1 2 "' " } {XPPEDIT 18 0 "Bi^212;" "6#*$%#BiG\"$7#" }{TEXT -1 7 ":n ja '" }{TEXT 261 1 "4" }{TEXT -1 2 "' " }{BITMAP 39 15 15 1 "?TMgW:B:nH>?:[Z:F:C:;: :JB;:jB@kB<<;r>]BGB::@K JB:@[M>B<:ZKB:B:D;B::@KSD;C:]ZLF\\ZR:]b>=S>cSB]BG;R>;kBb>;B:>ZK>^>?b>bLN<_b:aBJ::@JSDkCDLC@jR>:;::]j:@KJN<1:" }{TEXT -1 214 ":n vastaa viin suureisiin. Ratkaistaan hajoamisketjun differentiaaliyht\344l\366 ryhm\344 ja piirret\344\344n kuvaaja ytimien lukum\344\344rille ajan s uhteen. \n\nYtimien hajoamisia ja toisikseen muuttumista kuvaa seuraav a normaaliryhm\344. \n" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 189 " ryhma1:= diff(n[1](t), t)=-lambda[1]*n[1](t), diff(n[2](t), t)=lambda[ 1]*n[1](t)-lambda[2]*n[2](t), diff(n[3](t), t)=lambda[2]*n[2](t)-lambd a[3]*n[3](t), diff(n[4](t), t)=lambda[3]*n[3](t);" }}}{EXCHG {PARA 0 " " 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 80 "Ongelman tuntematt omat funktiot ovat ketjun eri alkuaineiden ydinten lukum\344\344r\344t ." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 54 "tuntemattomat1:= \{n[1](t), n[2](t), n[3](t), n[4](t) \};" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 38 "Alkuehdon m\344\344ritt\344\344 tilanne, jossa on " }{XPPEDIT 18 0 "10^16;" "6#*$\"#5\"#;" }{TEXT -1 5 " kpl " }{BITMAP 39 16 16 1 " ?TMOX:B:nH>?:]:=J\\:B:jyyyyK:VquXQKF\\KNquXqK::::::::?cB?CJ?cB;d :?cB^[F\\K^@>:ZK>^;N\\;>^Lb>_:;:R>B:D;B:;:R>ZMN^LJ:< :ZK:@jBD;;B::@KS@LCJ:D[:B::@kB^@DLKD;<:ZK>>aBJ@kB^ :F\\ZB:;Z;j:@KC:V\\L>ZMN<=BB?S>_SB:FZZ>Z;bB=CG]R>]R>;K :<:FZnR:cS>D;<:Z<>bLNZ:O\\KF^ZJ::R:;c>=JCF`ZJ::R:_c>=bF:;::]ZK:1: " }{TEXT -1 19 " ytimi\344 (n. 3.72 \327 " }{XPPEDIT 18 0 "10^(-6);" " 6#)\"#5,$\"\"'!\"\"" }{TEXT -1 4 " g):" }}{PARA 0 "" 0 "" {TEXT -1 0 " " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 59 "alkuehto1:= n[1](0)=10^ 16, n[2](0)=0, n[3](0)=0, n[4](0)=0;" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 63 "Ratkaistaan differentiaaliyht \344l\366ryhm\344 ja sievennet\344\344n tulokset:" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 64 "rtk1:= dsol ve(\{ryhma1, alkuehto1\}, tuntemattomat1):\nsimplify(%);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 59 "maarat1:= subs(rtk1, [n[1](t), n[2] (t), n[3](t), n[4](t)]):" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }} {PARA 0 "" 0 "" {TEXT -1 28 "M\344\344ritell\344\344n hajoamisvakiot: " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 84 "lambda[1]:= log(2)/3.6;\nlambda[2]:= log(2)/(10.6/24) ;\nlambda[3]:= log(2)/(61/60/24);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 110 "Piirret\344\344n kuva ainem\344 \344rien muuttumisesta ajan funktiona. Tarkasteltavana aikav\344lin \344 k\344ytet\344\344n yht\344 kuukautta." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "with(plots):" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 164 "display(plot(maarat1[1], t= 0..30, color=red), plot(maarat1[2], t=0..30, color=green), plot(maarat 1[3], t=0..30, color=blue), plot(maarat1[4], t=0..30, color=cyan));" } }}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 13 " L\344ht\366ytimien " }{BITMAP 40 17 17 1 "?TMOX:B:nH>?:]:=J\\:B: jyyyyK:VquXQKF\\KNquXqK::::::::?cB?CJ?cB;d:?cB^[F\\K ^@>:ZK>^;N\\;>^Lb>_:;:R>B:D;B:;:R>ZMN^LJ:<:ZK:@jBD;;B::@KS@LCJ:D[:B::@ kB^@DLKD;<:ZK>>aBJ@kB^:F\\ZB:;Z;j:@KC: V\\L>ZMN<=BB?S>_SB:FZZ>Z;bB=CG]R>]R>;K:<:FZnR:cS>D;<:Z<>bLNZ:O\\KF ^ZJ::R:;c>=JCF`ZJ::R:_c>=bF:;::]ZK:1:" }{TEXT -1 59 " (punainen) h ajoamisessa syntyy ensin vihre\344ll\344 merkittyj\344 " }{BITMAP 39 16 16 1 "?TMOX:B:nH>?:]:=J\\:B:jyyyyK:VquXQKF\\KNquXqK::::::::?c B?CJ>Z^N^:K::F\\KF\\ZJ:HkBL=<:ZK>>;\\::R>@JJB::@;b[>><:ZK>^;V\\:S>_c>B::@KJ]BBDJKLL;DLZDJK>ZK>>]ZL> Z:R:]b>=R>;S:]J:@KJDjB<;b>V_SB_J:D;;B:=BBj:F\\KR>;C:?b>>Z:FZ nb>F:;J:DJZD[Lb:;\\:B::@JJDK;D[;J:B::@JSDk:D[;N@;B:<::]J:D;]5: " }{TEXT -1 54 " ytimi\344 jotka nopeasti hajoavat sinisell\344 merkit yiksi " }{XPPEDIT 18 0 "Bi^212" "6#*$%#BiG\"$7#" }{TEXT -1 92 " ytimik si. Niiden puoliintumisaika on kuitenkin niin lyhyt, ett\344 ne hajoav at hyvin nopeasti " }{BITMAP 39 15 15 1 "?TMgW:B:nH>?:[Z:F:C:;::JB;:jB@kB<<;r>]BGB::@KJB:@[M> B<:ZKB:B:D;B::@KSD;C:]ZLF\\ZR:]b>=S>cSB]BG;R>;kBb>;B:>ZK>^>?b>bLN<_b:aBJ::@JSDkCDLC@jR>:;::]j:@KJN<1:" }{TEXT -1 114 " ytimiksi. Jo vi identoista p\344iv\344n kuluttua l\344ht\366hetkest\344 on j\344ljell \344 l\344hinn\344 vain vakaita turkoosilla piirrettyj\344 " }{BITMAP 39 15 15 1 "?TMgW:B:nH>?:[Z:F:C:;::JB;:jB@kB<<;r>]BGB::@KJB:@[M>B<:ZKB:B:D;B::@KSD ;C:]ZLF\\ZR:]b>=S>cSB ]BG;R>;kBb>;B:>ZK>^>?b>bLN<_b:aBJ::@JSDkCDLC@jR>:;::]j :@KJN<1:" }{TEXT -1 91 " ytimi\344. Eniten niiden syntymist\344 hidast aa l\344ht\366ytimien verrattain lyhyt puoliintumisaika. " }}{PARA 0 " " 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 5 "" 0 "" {TEXT -1 7 "Teht\344v \344" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 83 "T estaa puoliintumisajan vaikutusta radioaktiivisessa hajoamisessa. Mik \344li puolitat " }{BITMAP 40 17 17 1 "?TMOX:B:nH>?:]:=J\\:B:jyy yyK:VquXQKF\\KNquXqK::::::::?cB?CJ?cB;d:?cB^[F\\K^@> :ZK>^;N\\;>^Lb>_:;:R>B:D;B:;:R>ZMN^LJ:<:ZK:@jBD;;B::@KS@LCJ:D[:B::@kB^ @DLKD;<:ZK>>aBJ@kB;C:]Z:>:@:=R>_RB]BG@KJDjB<<;:ab>;r> _b>DKK@KS@<>:FZZR:HK[DkBR>;K:<:FZnR:cS:]CB>::DJZDK;^LF:_ jJ<<;:Z;N`LFZljR<<;::]J:@;_5:" }{TEXT -1 128 ":n puoliintumisajan, kui nka paljon v\344hemm\344n ytimi\344 on j\344ljell\344 4 puoliintumisaj an j\344lkeen verrattuna todelliseen tilanteeseen? \n" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 50 "Mik\344li haluat tutustua tarkemmin radio aktiivisiin " }{URLLINK 17 "hajoamisketjuihin" 4 "http://www.uic.com.a u/neAp2.htm" "" }{TEXT -1 36 ", voit tutustua niihin Internetiss\344 \+ " }{URLLINK 17 "Uranium Information Centre" 4 "http://www.uic.com.au" "" }{TEXT -1 85 "n kotisivuilla Australiassa. Loistava laskuri hajoami sketjujen simuloimiseksi l\366ytyy " }{URLLINK 17 "Project Java" 4 "ht tp://www.journey.sunysb.edu/ProjectJava" "" }{TEXT -1 60 "n kotisivuil ta, miss\344 yksi ohjelmointikilpailuty\366 keskittyy " }{URLLINK 17 " hajoamisketjun laskemiseen" 4 "http://www.journey.sunysb.edu/ProjectJa va/Radiation/home.html" "" }{TEXT -1 2 ". " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 262 24 "JP & SKK & MS 12.07.20 01" }{TEXT -1 0 "" }}}}{MARK "0 0 0" 0 }{VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }