. ا ان ا
اء :
د اة -1- 1 -1 :
2 1 2 1 2n n n nC H COOH HO C H COO H O− −+ ++ → +
-----------------------------------------------------------------------------------------------------------------
2 1 3
23
. 10 . .15.101,5.10 /
10.10B B
AA
C V mol L LC mol L
V L
− − −−
−= = = ⇐ . .A A B BC V C V= %#ل #" ا! -1-2 :
2 1
0,45060 /
. 1,5.10 . .0,5A o
m gM g mol
C V mol L L− −= = = &'. : و .Am M C V= ⇐ .A
n mC
M M V= =
') :
2 2 2 2n nC H O+ + 2 -,'& ا+* 1n nC H COOH+ 1 /32 ا 1آ/. : ا!/ ا M 4: 12 12 2 2 32 14 46M n n n= + + + + = + : ذن آ!/!& ا1 إ
. 3CH COOH : -, ا32 ه. ⇐ 60 46 14
114 14
n−= = = ⇐ 14 46 60n + = : إذن
----------------------------------------------------------------------------------------------------------------- 2- : ا;(ول ا1-. !:(م ا! -2- 1
10 .pH
fx V−= ⇐ 3 3 10 pHf
f f
xH O CH COO
V+ − − = = =
[ ] [ ]3 3
3 3
10 101 .10
10 10
pH pHpHf A f A
ApH pH
f f
CH COOH CH COOHC CC
CH COO CH COO
− −
− −− −
− −= = = = − +
[ ]3
3
1 .10pHfA
f
CH COOHC
CH COO −= − +
-------------------------------------------------------------------------------------------------------------- 3 3/CH COOH CH COO − >دو/ * :
2Apk 2-2-))3
: أي [ ]2
3
3
log fA
f
CH COOpk pH
CH COOH
− = − ⇐ [ ]2
3
3
log fA
f
CH COOPH pk
CH COOH
− = +
[ ]3
3
1 .10pHfA
f
CH COOHC
CH COO −= − +
: و?/ أن
[ ]2
3
3
log fA
f
CH COOHpk pH
CH COO −= +
2log( .10 1)pH
A Apk pH C= + − : إذن
2
2 3,33,3 log(1,5.10 .10 1) 4,76Apk −= + − = : ع .ت
------------------------------------------------------------------------------------------------------------ 3-
3NH : و 3CH COOH 1 -3- د ا! اDي 3(ث
3 3 3 4CH COOH NH CH COO NH− ++ → +
------------------------------------------------------------------------------------------------------------ 2-3 - E ! ا!1ازن ا:و? ! اG :
------------------------------------------------------------------------------------------------------------
:'H *(ول :(م ا!
max
.1
1
of
o
kn
x kkx n k
τ += = =+
.IJ'ا!:(م ا K? :
. ا! آ/. ⇐ 3
3
27,5.100,994 1
1 1 27,5.10
k
kτ = = = ≈
+ +: ع.ت
------------------------------------------------------------------------------------------------------------ .L?1د ? ز ا;>ء اM?. : ا
د ا! ا3- %#ل اN!,ل ا1د -1 :
2
, 2
.1
.r i
Zn C VQ
C VNi
+
+
= = =
1- .I)Kا رج ا!% : 1
. . ا'R3 اK1Q!Nر ا! ⇐ ,r iQ k<
------------------------------------------------------------------------------------------------------------ أن - 2-1 1د أي اS?1د / T ا TQ:ا M. ا! !1Qر . ا'R3 اKW ،Nن إ!ود ا>?V! Lآ( ، إذن
1د أي ا1د إ!د ا'وأ1?ت ا' X!>ل ، إذن / T*1M ا:TQ ا . %رج ا1د .I Jر ان ا!W &'و .إ!ود ا>?L ?13 إ!د ا'
------------------------------------------------------------------------------------------------------------ 2- . /> ا>?L وX!>ل أ1?ت ا' آ(V! %#ل اN!,ل ا1د - 1-2
(ة اN!,ل ا1د M أ1?ت ا' آ!/ ا+!ود 1*( 1 ة Wن أن ))3 ''.ا! ا3( اDي 1Hف 2 2Ni e Ni+ −+ →
( ) 2. .n e C V− = ⇐ 2 ( )( ) .
2
n en Ni C V
−+ = =
max
2. . .C V Ft
I∆ = ⇐ max max. ( ).Q I t n e F−= ∆ = : و('
2 1 4 1
max
2.(5.10 . ).0,1 .(9,65.10 . )9650 2 40 50
0,1
mol L L C molt s h mn s
A
− − −
∆ = = = : ع.ت
------------------------------------------------------------------------------------------------------------
#ل ا;(ول ا1Q! .-1ر ا! ا3- %#ل اN!,ل ا1د :
(1) ( ) ( ' ) 'i f i fn Ni n x n x∆ = + − = دة ا' ا!1ن %#ل (ة ا\N!,ل: آ
2 2Ni e Ni+ −+ → : و(' %#ل ?^[ اد
(2) ( )
( )2
n en Ni
−
= دة ا' ا!1ن %#ل (ة ا\N!,ل : آ
.
( )I t
n eF
− ∆= 4 :( )
2f
n ex
−
= ⇐ )2)=(1(: إذن
.
2.f
I tx
F
∆= &': و
-------------------------------------------------------------------------------------------------
d
λθ = 1-
------------------------------------------------------------------------------------------------- 2-
2
Ltg
Dθ =
2 D
Ld
λ= ⇐ 2
L
D d
λθ = =
------------------------------------------------------------------------------------------------
λ : وي 1( )fd
θ = R'3'/ &*1 اا ⇐ d
λθ = أن-1-3 - 3 :
2
64 1
(0,44 0).100,44.10 0,44
1 (1 0).10( )
radm m
md
θλ µ−
−−
∆ −= = = =−∆
8 114
6
3.10 .6,82.10
0,44.10
c m sHz
mυ
λ
−
−= = =
----------------------------------------------------------------------------------------------- 2-3-
. 800R nmλ = S400 واV nmλ = ا;ل اI. /`1ء 13ر اK';. - أ
ض اK: اآ>" R^"أ E دي ا/1ن 1اS1* /`1ء ا. Wن أآ1b Kل 2 DL
d
λ= أن ض اK: اآ> :
. 800R nmλ = Sإذن ا`1ء ا
----------------------------------------------------------------------------------------------- .I⇐ واآT و-1ل *4 اNS ا`I1 /`1ء ا 0θ = ، 0L = 'K ل -ب &?S 2 : 1ن وdH اK: اآ> أ
]/!X 2 Sا/1ن ا .Q 1انSا . -----------------------------------------------------------------------------------------------
1-1-
L Ru u E+ =
. .di
L r i R i Edt
+ + =
. ( ).
.
diL R r i E
dtL di E
iR r dt r R
+ + =
+ =+ +
I. . ا(ارة Jر اة ا!)N J::3 .!ا /e!د ا: ا
L
R rτ =
+ 4:
-----------------------------------------------------------------------------------------------
/e!د ا !21 . ا :
)' .?Mف اQوا )' :t
e τ−
. !E:3 هfD ا#" ;T أن 1ن
./ : و T! LD ا3 آ
L
R rτ =
+ 4 : 1
tEi e
R rτ
− = − +
-----------------------------------------------------------------------------------------------
R/ ^3? 1tE
i eR r
τ−
= − + و 21 . ا#" إR ا^
t
e τ−
ول و +∞ Rإt )'Iم ا(اg'ا E:3! ول
. 100oI mA= : ، وه. K? وي o
EI
R r=
+ Iم ا(اg'ا . .I Jر اة ا!)N ":
4r = Ω ⇐ 2,4
20 24 20 40,1o
Er R
I= − = − = − = Ω ⇐ ( )oI R r E+ = ⇐ o
EI
R r=
+
2,5msτ = ⇐ oi I= 4 ا:رب 0t = g3/ا )' R'3س / ! ا> ?:: Q4b اG ?K
3( ). 24.(2,5.10 ) 0,06L R r s Hτ −= + = = ⇐ L
R rτ =
+
----------------------------------------------------------------------------------------------- 1-2 - 2-
. 2D أي RLC TQ:ا .I'G E 1ا ( أ( R'3'⇐ ا د?1 '( ا? " D%V Z ?ا'K R'3 أن ا
----------------------------------------------------------------------------------------------- 2 2( ) ( 2 )oZ R r L Nπ= + + ذي ا ? : 1D ?M !,ات ) ا ب( 2-2-R'3' %#ل ا
1000oR r+ = Ω : أي 1000Ω iل ا#% ?K!J 3 و" : oZ R r= + : 1D ? jK^ 0N = 'K /!دد
996oR = Ω ⇐ 1000 1000 4 996oR r= − = − = Ω &': و
2
2 1( ) .2
.2 .oo
Z R r L NC N
ππ
= + + −
ذي ا ? : 2D ?M !,ات ) ا أ( %#ل
R'3' ا
2
1
.4oo o
CLC Nπ
= ⇐ (a) 2 2.4 1o oLC Nπ = : أي 1
.2.2 .o
o o
L NC N
ππ
= ? د?1 إذا آن : 1ن ا
92 4 2
14,22.10 4,22
0,06.(4). (10 )oC F nFπ
−= = = : ع.ت
----------------------------------------------------------------------------------------------- 3-2 -'3' : '( ?:: Q4b ا
⇐ 'Z Z= :و('
2
1
8. . o
NC Lπ
= ⇐ 2 28 . 1oN C Lπ = ⇐ 2 Nω π= 4 :2 2
2 1
. .o o
L
C C ω=
1
2 2 o
NC Lπ
= : أي
1
2o
o
NC Lπ
= ') : 2 2.4 1o oLC Nπ = (a) ل#%
2oN
N = &': و1
2o
N
N= :إذن
-----------------------------------------------------------------------------------------------
1— g!' Iدا .'Q-\ا .'K أن آ ا:
bف اSرض . ا*4 اآ>ي اSرX .e`4 ا: ا\-Q'. %#ل آ!& &/ :KQ:إR "1ة ا!;ذب ا1?. ا
آ> . ا?;Dا2
.. Tm m
F G nr
=
1' .?M?1ن اا: EKQ! : .F m a=
2
.. .Tm m
G n m ar
=
0t
dva
dt= = ! G &!H نW رضl K' أن ا: ا\-'QH .آ '(م . .H.و m!'!? LD أن ر& ا
2
n
va
r= ، t n na a a a= + =
J;! .' / أن . :ا!رعو
. r JN g!' .'Q-\ا n إذن آ ا:G Jg'آ> و !;J ا!رع ا?;Dا 2
. Tn
ma a G n
r= =
2
2
.. .Tm m v
G mr r
=
2 . Tmv G
r=
. Tmv G
r=
v rω=
3
1 T Tm mvG G
r r r rω = = =
322
. T
rT
G m
π πω
= = : ا(ور
-----------------------------------------------------------------------------------------------
2 2
3
4.
. T
T
r G m
π= ⇐ 2 3
24. . T
T r
G mπ= 2- : %#ل ا#" ا :
24.
. T
kG m
π=
-----------------------------------------------------------------------------------------------
%#ل اQت :
4`X .!رض اSا R/ 1' .?M?1ن اا: EKQ! oiف اb J/ :KQ::1ة ا!;ذب ا1?. ا
/ .S T GF m a=
2
2
.. .T S T
TT T
m m vG m
r r= .g' \H:ط /R ا :
32
2.T
TT T
rT
G m
π πω
= = ⇐ 3
1 S STT
T T T T
m mvG G
r r r rω = = = ⇐ . S
TT
mv G
r=
2 3
2
4. .
.T
ST
rm
G T
π= : و 2 2
3
4.
.T
T S
T
r G m
π= ا : !ل ا ارضآ ن ا
آ ورأ# "ن : ارض !ل ا()'&%ا ان ا
2 3
2
4. .
.T
rm
G T
π= ⇐ 2 2
3
4.
. T
T
r G m
π=
23
.S T
T T
m r T
m r T
=
: و'& ?!Xج
24 1oT T h j= = = #q أرW .eن دورf وي دور آ اSرض 1ل ?J : ع. ت K' أن ا: ا\-'QK .(و Hآ' :
44,22.10r km= ، 81,496.10Tr km= ، 365,25sT j=
2 3 23 8
54
1,496.10 1. . 3,34.10
4,22.10 365,25S oT
T T
m Tr km
m r T km
= = ≈
-----------------------------------------------------------------------------------------------
1-
. 1m M+ : J!/!آ C1 ;1رة + ا^:1 ا(روH ا; ا
1 '( ا!1ازن /:1ى ا! : ; X`4 ا : 1;. وزن ا P
.jQH GV ا!س : R
. 1R :2 bف ا' :KQا:1ة ا 1F
. 2R :2 bف ا' :KQا:1ة ا 2F
0FΣ =
!N EKQط ا!1ازن :
1 2 0F F P R+ + + =
: ox R/ ط:H+
1 2 0 0 0F F− + + + =
2 1k k∆ = ∆ℓ ℓ ⇐ 1 2 0k k− ∆ + ∆ =ℓ ℓ
----------------------------------------------------------------------------------------------- "K*. x 4 : 2 ( )oF k x= ∆ −ℓ : و 1 ( )oF k x= ∆ +ℓ : %#ل ا3آ -2
: 1' .?M?1ن اا: EKQ!
-----------------------------------------------------------------------------------------------
3- 1-3 - ./ : اد ا!e/ ا : !T آ
. 0t = )' g3/ا : 0x = i2%#ل ا ') :
2
πϕ = ± ⇐ cos 0ϕ = ⇐ 0 cos( )MX ϕ= :إذن
0t = )' 0v < ⇐ ox :!' R3' o . 1;ا 0t = ، '(%#ل ا'R'3 و
. 2
sin( )Mv x x tT
π ϕ= = − +
2
πϕ = + ⇐ 0ϕ > ⇐ sin 0ϕ > ⇐ sin( ) 0Mv x ϕ= − < ، 0t = )'
-----------------------------------------------------------------------------------------------
%#ل اد ا!e/ /3آ - 2-3 :
122
m MT
kπ += ⇐
1
2o
k
m Mω =
+ ⇐ 2
1
2o
k
m Mω =
+
----------------------------------------------------------------------------------------------- 1T s= 3-3 - ') ?K:
2
12 2
4. ( ). 0,3 .4.(10)6 /
2 2.(1 )
m M kgk N m
T s
π += = = ⇐ 2
124 2
m MT
kπ+=
----------------------------------------------------------------------------------------------- 3-4
1H E/! \ 1ى !/!J و-# ا' 2ا(ور ;.اXص / -----------------------------------------------------------------------------------------------
4-4-
⇐ 2
2 22
'
4 2
T m M
kπ+= ⇐ 2
2 ' 22
m MT
kπ +=
********