. 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 +=

********