1

23 2009

:!" #$

%& '( :3h )$ 7

$*& + * , - .

/ #(0 " / 12 3 / 1 45 67 89 6 : ;&"<

1 =>14 : ?67 @ .

B&

/5 %7 2C / )$ > %3D (: $ %31 %C E ;FD ).

GH& IH JKL M($ ;0 J N> ) :

I : %O 2P /$ J Q2 )K"

II : 2 )F "M"

III : ;ST (

IV : ;!J U GJ* =K '!V +2

2

23 2009

– òîöbíŒîÐÛa@âìÜÈÛa@ñ…bß@¿@†yì½a@íŠvnÛa@æbznßüa@@@< <

!"# $ % & :($)* +, -& '( 3;K*

V )$ :7

I : %O 2P /$ J Q2 )K" Le Réacteur nucléaire naturel d’Oklo au Gabon

! !W /$ J #2P %3 )3 Y E :( 238U ) ': 99,2745 %(

235U ) ' : 0,7200 %( ) 234U ' : 0,0055 % (

W 2 ;[K" / )$ 23592U J\M:]#2P )H1 /3 /$ J #2P EH^1 E 6 235

92U

3 %24 %. #2P 235 #2P 2 238 / =K @"H K 8"V /K$S> _\ @7002 * %4,47 * '2 " 72 / C +2P `01 % aP %31 62U(235) ( #2P '2 %L bc $ 2C ]235

%d -K /7 C ` (: /$ J #2P /. $ J ' (01 ) * Q ) : U(235) 01 3,5 %.

e / %C , 2C #2P (01 %O 235 f 0,440 % +( % 072. '2 /(1 " U(235) 5" %O e $ J , : Q2 )K" MF2" /$ V "/ )O\ g: 67 .

)K" 2 H$ 2 ;[K" 22 *(@ ; 0 "/$ J " MF2 hU[ %O+ $"1 '2U(235) / e J* ' g 0 g: E:0,44 % 6 )$ Q2 )K" MF2 ` 72 1,7* !

%31 U )$1 / /7 ? iJ J\[ ;21 U .+ '2 ;j kV MF2 "U(235) $"1 l* K +&1U(238) #1 => %21 -"01 ($ 239 => ?2( +& Q62U(235)] /7 m" ;&/

2 ;[K" / n(&1#1 oD H$ .

;J$ :JeVmolgUMsanmolN A

1912357123 10.6,11;.235)(;10.31;10.6 −−− ====

M($ 1 2 3 4 5 6 7 8 9

e,

Q (Ln)

0 0,7 1,1 1,4 1,6 1,8 1,9 2,1 2,2

1. e@ p

1.1 /$ V Q2 )K" K ' K %O e / n(& K 3 Q6 SY M(U.

1.2 (K> q0 U(238) 2 ;[K" /J$ %C 3 %21:

(4) ... (3) ....u

(2) e p )1(

235

92

239

94

239

94

239

93

0

1-

239

93

239

92

239

92

238

92

+→+→

+→→+

UPuPNp

NUUnU

;[K" )$1 %2( %N2(3)2 (4)/K$SD _\ 4 => \ k!:(2 )K" 6@ EUH

1.3 W %C +0" EHb " JS W -K (1 j> )K"1 Q2(U2 C 2C . %C U(238) EHb .

2. p: /K$SD

12 (1K J/K$SD _\ %0 gr^ $\ :N = N0 e-λt sU λ K$SD . l1 / :[$ ` Cλ 8H $ t1/2

22 (MK (U2 $ e: M(U p 'M ;$ =K #2t K$SD 235) K $t1/2 QM($ k J 67 /

(an) .(

3

32 ( #2P '2 p:1 %C ) 0235 3,5% => 0,72% #2P u M($ p:1 @0 235 )$8 . '( M(U∆t /

;J$ k1 ?67 )7 ] p: 67 @ Jv

3( :J U qV )K" Q2

;[K"1 J\ 3 / n(&1 / )K" Q2

n3SrXenU 10

9438

13954

10

23592

++→+

Xe : 2 %3Sr )K" 67 K 1 :J #12* Q=120MeV

13 ( k!:( K $ f 2 " /MeV/c2 . Q21 )1 MeV/c2 Q21 :V 7Y311 MeV . O1 lKC∆m

-: EU e ] Q2 )K" +[b K.

23 ( Q2 M: @ Q2 )K" /m1 = 2350 kg U(235) '( +[b ∆t1 = 3 ans +OS .

123 ( u M(K M(UN1 '( ?67 +[b J\ .

223 ( 1 :J EUEf MeV + e .[K" ) %C ) 0; :J m" 01 w1 Q.

323 ()K" 6@ & J* '(0 w* .

II : """" 2 )F 2 )F 2 )F 2 )F " " " " M M M M L’eau de Javel et l’eau de Dakin

;J$:

2P N, eU )@ / :5

1

;F2M: ClO (aq)− /Cl(aq)

−2 O2(g)/H2O(l).

3 ;NO :R=8,314u.S.I

(K /P 6 25°C : Ke = 1,00.10-14

$* P !3 M )F ($] =K Q& /! -& `3 `&1 ;CClO (aq)−

C2 23 ;Cl(aq)−

;C2Na(aq)+

(2(@ ;C2 HO(aq)−

. )F q$ `3 `&1 %P )r" e0$ (Y2 Q(K: gV 2j %d m" /

24 V^ P2 ( @J )O ] ;(H / e* `&1"M +&"liqueur de Dakin

+2P : 3 &Q )F 3"12 ! .

/!3 +& k2 `3 `&1 ;P '(C kV K )F 3"xJ xJ xJ xJ 2 /3/3/3/3 -M$ :

)(2)()( 22gaqaq OClClO +→ −−

8"^ 3" 6@ / J g 5 ; & Q +(S0)r& s(U eU =K )H& V = 250ml +& (S1).

EH e y [<C 76^ W& (K 0 )O\

V1= 20,0ml+& (S1) FU / g51 /2

/ -1U FM > /

T = 300 K (K m0 E* N@F J*2

"^ ;W&t F& / NO lO5 P(t)0 )

@.

;NO ) $ . eU =0 - +& +[b

/ F&V0 . (K /!( lOr t = 0

min f P0 :

1.1 ( E +b2 '(t 23D M$

)F 3"1 )K" 0 .

12 (/J$ U 2( /!3 +& /"< s 010203 ,, nnn !( 'M ; / =KClO (aq)

−2Cl(aq)

−2O2(g)

4

t (min)20 40 60 80 100 120

x (mmol)

0.2

0.4

0.6

0.8

1

112 (j n022 n03, ($ .

212 ( K Kn0 !( 'M ( NO 3 K K e ;J$ n03 ( n0

312( /!@ #(0 K Kxf e )K" 6@ !@ & ((&1 g k +2( e1C.

13 ( #(0 @00& / :[$ ` C /"< +2( +$*x(t) / )3\ =K E31 /2 :

( )TR

VPtPtx

.

.)()( 00−

=

14 (#(0 fU z3 K J1 +[b lOr : x(t) )3\ =& lb -2 1) F-(

114 ( & K qK v(t) W& (K 7 $1 lK2t

214 ( J 67 K +2Y /& )$ M(U ] +[b )K" K* J1 8.

314( Q )F 0H =K C0 (S0) `3 `&1 ;P / :0

2 1

( ) 5,0.10 .aqS

ClO mol L− − − = . M(U :

n01 . j )K v 1 @ k0& o =K 'SD )7 .

2. / : +& *M""M "

f - Q62 8"^ )F => 5> Q& Q62 @J 67 *M .0(S2) #MH ;F2(7 +&

3NaHCO ;F2(7 ;C 1 s&

/ =K - ;3 ;C23,00.10-1 mol.L-

1 2 3,00.10-2 mol.L-1.

12( `&1 %P k & FD OH EC

`3ClO (aq)−

. r& qKKA1

7 $1 lKC e F2M .

22 ( %C KpH +& (S2) Q210,3 pH1=

%C2pKA1 = 7,3 . K K[ ][ ]HA

ClO−

sU[ ]HA

+ k & 1ClO(aq)−

.jv w1

32 ( F2M U 7 ;F2(7 %P

HCO3(aq)− /CO3(aq)

2− @rU KA2 sU

pKA2 = 10,3 . . )K"1 n(& /!

HCO3(aq)−

;C2HO(aq)−

+& (S2).

132 ( )<& )K" M$ ECHCO3(aq)−

2 HO(aq)−

.

232 ( k %N K KK ( KA2 2 Ke 7(: 1 M(U2 .

42(

142 ( %C f& ` CpH M +& -: pH2 = 9,3.

242 ( j pH O<C 8W 67 pH +& (S2).

342( '(( EUC [ ][ ]HA

ClO−

.

442 ( )F +( V^ P2 .2 @J2 8W M +& +$* GF (U2 $0 * lKC.

5

1111 III : @3 @3 @3 @3 : : : : ;SD ( ;SD ( ;SD ( ;SD (Un générateur de signaux

*M .0O1 3 N@F 2M 'SL O< ;H 3 6 . =1 23> =K N@ 67 ($« trigger de

Schmidt » 83 / =K E1 K ' K /72 N@ 6@ J 1 - F )3\ ) ] *( ?67 / M2 , @OS C(

202R = 10,0 kΩ 23D 2

83 /V 1 (K 0uc = 15,0 V (KH1

)'(K< 11 1 ( -V 1 %3 )< 23D qH1U = 0,0 V 83 /V 1 (K2

0

uc = 5,0 V N1 ) N 11 1 ( qH1 &@3 -1: ( 23D E =20,0V . /V / )3\ )

23D u(t) 832 uc(t)

1 ( E +OS C(

11 ( 1 =K q$1u(t)2 uc(t) F [$ .

21 ( ?6b91 Q6 =& )Kuc(t)2 u(t)

2 ( 83 &S *M.

W& (Kt = 0 s 83 %3 y [<C 76^

23D /V 1 %32 %&\ , u = E

= 20,0 V . )3\ =K '( k E o6

- F

12 ( 1 @00& / 5" M$ ` Cuc(t)

22 (%C k0&1:( ) ( )τ/1 t

c eEtu −−= 5" M$ )U

0 $1 M(& τ ( ;J$

32 (+ ) =& =K MKuc(t) %C | ms10=τ ) ((& $ 0J )1τ (

42( w* : $* 83 C

3 (3D 2M 2« trigger de Schmidt »

13 ( (K )< qH1 23D %P " 83 00& /

G H : : : : 3

15,04

cu E V= = 0 0 M(U

W&t1 / 23D 7(K GF9 . V2t1 + ) )3\ =K uc(t)

23 (&\ e :[J t =0 s %P

:[J > ( qH1 23D

15,0

4cu E V= = W& K K t2 GF91 /

$1 :[J @uc(t) M$ )U

0 5" . V2t2 =K )3\.

33 ( + '( M(U /1 %C k0&12T

=22ms

43 ( 2( "^1 (T 1 uc(t) +( *

O<C #C C $* +$* E )7 83

)K v 0 $.

Trigger de Schmidt

u

uC

uR

10,0

kΩ

t (ms)10 20 30 40 50 60 70 80

Uc

5

10

15

20

6

1 IV3 :1 : : Etude d’un appontage

1( & @B =K '!J +2 U *M:

!V + 0* U )$2 ;!J U @B =K ;

'!J U G 3 + UC #(^1 (F 'O< 8:

qJ (O.

)@ 0 UN> K ' K '!J U %C $

'0 9 e1 8: U %C $2 ;3U ) @[b

F

/2 '!J =K + UP 91 +[b @1(S $.

W& 6^ qJ => '!J +bMO o( J0 (K y [<C r" e$ [<C 76^ (O,X) . '!J m =

1,2.104Kg .

W& (K ,0 s t = 2 0 N M( +[b '!J < 6b9 ∆t = 0,10 s . & k2 '!J 7(< e1 '(U2 J0

(O,X) / +2( /J$ ] W& ( J0 ?67 )<Ct =2,0s .

t (s) 2,0 2,1 2,2 2,3 2,4 2,5 2,6 2,7 2,8

x (m) 70 74 78 81,4 84,1 87,0 89,2 90,8 92,3

v (m.s-1

)

1 ( K EUC :2 =K -0 e +2( / @2M2 W&

2 (- F =& ) ))3\2( / + / '!J U $ V M(U ] ;K lJ^ [2,1 ; 2,8 s] رع a د ات ا

.

3 (" د ات ا!ة او !ن !ت$ ا# ة +. ا-,+*() '/ ل 012 ا*)

4 ( )3\ )2 J0 => @<2 W& '!J K* ;O1 Ol: g52 kV K @":1 W& => (capteurs) o( +V

_ @.

14( W& '(2 + UP _ 1 ) : '!J U $ V M(U + UP _ 1 W&2 o( m

24 ( / -K )H& lJ^ )7) )3\3 ( +Y w! k2 ( / + /[2,1 ; 2,8 s]. f )K

34 ( W& (K '!J =K + UP 9 20 '0 '(\ 0 0 M(Ut = 1,5s . $ 0J ~.

!" #$ 3 / -U %2(1*V

www.bibliophy.sup.fr

7

8

9

1 ( +2P :Q )F 3"12 !3 & .

1.10 +b2 '(t 23D M$

2 2

/

/

ClO Cl

O H O

− −

2

2 2

2 2

2 4 4

إ555555555555555555555555555556ال

أآ55555555555555555555555555ة

ClO H e Cl H O

H O O H e

− + − −

+ −

+ + → +

→ + +

12(

112 ( n022 n03($ , :

3" %CClO-MF2 M ? -C 2 / " " !( 'M ; %L -2 n[ 4P W& QC / er l^ %L )F

)3O22 Cl- 3*%($ , !3 K J1 *( [<C 76^ W& QC / .

212(

K $n0 'M !( 3

NO)K / MF @(:

;J$ EUO2 /7 @ / 1/5 -2 :

0 0 003

5 5 .

n PVn

R T= =

13 ( /"< +2( E3NO 'M 3 :

0 0

0 00 0

0

0 0

( ) ( ) ( ) ( )

( )( ) ( ), ( )

( ( ) )( )

T Tn t n x t x t n t n

PVP t Vx t Tو T و V V

RT RT

P t P Vx t و>55555555555555555555555;

RT

= + ⇒ = −

= − = =

−=

14 ( fU z3 K J1 +[b lOr : #(0x(t)

)3\ =& lb -21

114 (& K

:[$ )K" K* q$1:

214 (J 67 K +2Y /& )$ 2] +[b )K" K* J1.

0J 0 =& ;* -F )$1 K %L -2 +[b p: p:

+[b .

NO lO5 7 /!3 J 67 K +2Y /& )$ .

314 ( Q )F 0H =K C0(S0) `3 `&1 ;P / :

0

2 1

( ) 5,0.10 .aqS

ClO mol L− − − =

• :

0 00 0 0 0

.

.

PVPV n RT n

R T= ⇒ =

10

n0 = 0,2 mmol =2.10-4

mol

• ;J$ :

0

1

2( )

3 4

0 ( ) 0 0

5,0.10. . .20.10 2.10

5 5

aqS

aqS

ClOn ClO V V mol

−−

− − −

= = = =

2 . / : +& *M""M " 12 ( `3 `&1 %P k & FD OHClO(aq)

− '(K0 /7

& 0HClO

2 3

3

1

.aq aqéq éq

A

aq éq

HClO H O H O ClO

H O ClOK

HClO

+ −

+ −

→+ +←

=

22 ( ( :

( )

( )

1

( ) ( )

1 1

( ) ( )

( )

( )

( )10,3 7,3 3 3

( ) ( )

( )

log log

10

10 10 10 .

A

aq aqéq éq

A A

aq aqéq éq

aqéq pH pK

aq éq

aqéq

aq aq éqéqaq éq

ClO ClOpH pK pH pK

HClO HClO

ClO

HClO

ClOClO HClO

HClO

− −

−

−

−

− −

= + ⇔ = −

⇒ =

= = ⇔ =

'J /7 '(K0 ) 4@(

32(

132 ( )<& )K" M$HCO3(aq)−

2 HO(aq)−

: :2

3 ( ) ( ) 2 ( ) 3 ( )aq aq aq aqHCO HO H O CO− − −→+ +←

232 k %N K ( KA2 2 Ke 2

7(: 1

42(

142 ( fUpH M +&

242 ( %C j pH8W 67 ) M +&(O<C

pH +& (S2)))F (.

2

3

3 ( )

2

3 3 ( )

2

23 3 ( ) 3

14 10,3 24,3 25

2

.

.

1

. 1 1.

1

. 10 .10 10 5.10

aq éq

aq aqéq éq

aq aq aqéq éq éq

A

Aaq aq aq aqéq éq éq éq

A e

COK

HCO HO

H O CO HOKK

KHCO H O HO H O

K K K

−

− −

+ − −

− + − +

− − − −

=

= ⇒ = =

⇒ = = = =

2

3 ( )

2 2

3 ( )

2 1 2 1

3 ( ) 3 ( )

2 1

log

0, 3 . ; 3.10 .

0, 310, 3 log 10, 3 1 9, 3 10, 3

0, 03

aqéq

A

aqéq

aq aqéq éq

COpH pK

HCO

CO mol L HCO mol L

pH pH

−

−

− − − − −

= +

= =

⇒ = + = − = ⟨ =

11

'(K: F2M =K -!U M +&/ U/ :HClO ClO− ;C2 F2M ?67 U )K"1 n(& HO

-(aq)

p:1 E pH%C QC pH ?(U )F O<C M +& .

342( E& '(( [ ][ ]HA

ClO−

.

( )

( )

2 1

( ) ( )

2 1 2 1

( ) ( )

( )

( )

( ) ( )9,3 7,3 2 2

( ) ( )

log log

10

10 10 10 .

A

aq aqéq éq

A A

aq aqéq éq

aqéq pH pK

aq éq

aq aqéq éq

aq aqéq éq

ClO ClOpH pK pH pK

HClO HClO

ClO

HClO

ClO ClO

HClO HClO

− −

−

−

− −

−

= + ⇔ = −

⇒ =

= = ⇔ =

442 ( E g0 Q6)F +( V^ P2 .2 @J2 8W M +& +$* GF : 7 PH (

V^ P 2C ( =K Y1 %C @ 3 /2.

1( +OS C(

11 (23 qH1 ;J$ « trigger de Schmidt » 1 '( M2 (

11 l r :E = 20V 2E =0

I"2 &\ 83 gr^ @[b &\ (1 *C M K ' K 1 %32

N12 I" . %j>

21 ( %& )$1

/ +1

%31 (K 0 ( ) 5CU t V≤ ≤ qH1 ( ?11 E = 20V -2

&S U / 83 %3.

/ +2

%31 (K15 ( ) 20CV U t V≤ ≤ qH1 )< E 20V -2

3i3 '( %312 I"1 U / 83 % ) - F )3\(

2 ( 83 &S *M.

12 ( 1 @00& / 5" M$uc(t)

- F '( :

1

c R

c

c

c cc c

u u E

u Ri E

dudqi C

dt dt

du du Eu RC E u

dt dt RC RC

+ =

+ =

= =

⇒ + = ⇔ + =

22 ( )& k0&( ) ( )τ/1 t

c eEtu−−= ((&12 τ .

12

32 (

42 (: $* 83 C

:[$ RC τ= %C w

3 ( 23D 2M« trigger de Schmidt »

13 ( W& M(& t1 I" ) =&

( )1 1

1

/ /

/

11

2 3

1

1515 20 1 1

20

15 51

20 20

5 5ln

20 20

10 ( 1,39) 13,910 14

t RC t RC

t

e e

e

tt

t s ms

τ

ττ

− −

−

− −

= − ⇒ − =

⇒ = − =

−= ⇔ = −

= − − = ≈

23 (

U :[$: ( ) ( )τ/1 t

c eEtu−−=

( )1 1

1

/ /

/

11

2 3

1

11 1

4 4

1 31

4 4

3 3ln

4 4

10 ( 0,29) 2,910 3

t RC t RC

t

EE e e

e

tt

t s ms

τ

ττ

− −

−

− −

= − ⇒ − =

⇒ = − =

−= ⇔ = −

= − − = ≈

: - F )3\ WC

36

3

10.1010

10.10

RC CR

C F

ττ

−−

= ⇔ =

= =

/

/ /

*

1. (1 )

1 1 1 1( ) 0

tc

t t

du Ee

dt

E Ee E e

RC RC

E EE RC

RC RC RC RC

τ

τ τ

τ

τ

ττ τ

−

− −

=

+ − =

− + = ⇔ − = ⇔ =

13

33 ( f / ) =& 13 (

%C w 14 3 11t ms∆ = − =

-2 w %C2 11 22T ms ms= × =

43 ( :[KT 83 $

+ ) =& uC 2u :1 hU[p 2( T `H:1 RCτ =

p:1 w -2T $ p:1 => QMY

2( q$5DT $ q$5> %j> E

0* `$* / O<C $* 2j 83 +$* -2

1 3 :1 : : Etude d’un appontage

1 (K fU : v(t = 2,1 s) = (78 - 70)

(2,2 - 2,0) = 40 m.s

-1 +2( t 0J m"

t (s) 2,0 2,1 2,2 2,3 2,4 2,5 2,6 2,7 2,8

x (m) 70 74 78 81,4 84,1 87,0 89,2 90,8 92,3

v (m.s-1

) 40 37 30,5 28 25,5 19 15,5

1( 0 & %L -2 H:1 "1 M K ' K K ( #W iV .

4 @ ;:

• &(O,X).

• & =& m$ =&.

• a = ∆v

∆t =

(12 - 36)

(2,8 - 2,2) = - 40 m.s

-2

3 (1 / %0 :R P F ma+ + =

& =K _0*D(O,x):

4 5

5

0 0 1,2.10 ( 40) 4,8.10

4,8.10

x x x x

x x x

F R P ma

F ma F

F N

+ + =

+ + = ⇒ = − = −

=

'0F

& g 0 (O,X) @W2 & =& m$ =&2 54,8.10F N=

4 (

14 ( + UP _ 1 W&2 o( m W& '(2 + UP _ 1 ) : '!J U $ V.

14

K e1 W 0 & %L -2 & QN + UP _ 1 ) : K lJ^:170 .V m s−= . )H"1 / '(

/7 + UP _ 12 '!J m W&1t s∆ = . . 70 1 70d V t m= ∆ = × =

24 (

/ + / K ;O ) =&[2,1 ; 2,8 s] H:1 "1 M K ' K

-F )$ m" @ :a =

∆v

∆t =

(12 - 36)

(2,8 - 2,2) = - 40

m.s-2

)3WU[ /23 ( 2C g: m" K +H1 F 45 67 =K k$1 2C

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