.., .., .., ..

2

2000

53 (075) C32 22.3 .., .., .., ... 2: . - : , 2000. 66 . ISBN 5 - 88179 - 218 - 1

, , "", "", " , ". - 290700, 290300 550100 4, 5 6 . : ; .., ..-.., (). , 2000 .., .., .., .., 2000 ISBN 5 - 88179 - 218 - 1

3

. 3 .. 4 4 ...6 4. .6 6 9 4 ..24 5. .. 31 31 ...34 5 ...43 6. , .48 .. 48 ... 51 6 .. 56 ...62

- . . 3 : , , , . , , , , 4, 5 6. . , , . , : .. 999430 : , . . , 31, . 7 4

4

, . . , . , . , . , . , , , - . .

. , , , . ( ) , . , , . , .3, , . , , , . , , , .

1. . . . . -- . . . . . ( ) . . . . . . - . .

5

2. ( ). . . . . . . . . 3. . . . . - . . . . . . . . . 4. . . . . . 5. . . . . . . . . 6. . -. . . . . . . . 7. . . . . , . . . 8. . . . . . 9. . . . . . . . . . , , . . . . . . 10. . . . . . . . 11. . . . 12. . . . . . . . . . . . . 13. . . . . . - . - . . . . , . - . . - . . .

6

. . . . .

1. .. . - .: ,1985. 2. .., .. . - .: , 1989. 3. .., .. . .1-3. - .: , 1974. 4. .. .- .: , 1979 .- . 1-3. 5. .. .- .: ,1996. 6. . - - ( ) / .. , .. , .. , .. - .: , 1987.

7. : , - / .. , .. , .. , .. , .. ; . .. . .: , 1998.

8. .., .. / . ... - .: , 1978

9. .., .. . - .: ,1980.

4.

B H

B = 0H, - ; 0 - . = 1,

B = 0H. - -

[ ] 304 rIdd lrB

= lB dr

Id 20 sin

4

= ,

dB - , dl I; r - - , , ; - - .

RIB

20= ,

R - .

7

( ) 2/3222

0 24 hR

IRB+

=

,

h - , .

0

0

2 rIB

= ,

r0 - , . ,

( )210

0 coscos4

=rIB ,

r0 - , 1 2 - , . , , -cos2 = cos1 = cos,

0

0

2cosr

IB

=

.

B = 0nI, n - . , ( ),

F = I[l B], F = IBlsin, l - ; - B. . , :

dF = I[dl B].

pm = nIS, n - () ; I - , ; S - . () , , ,

M = [pm B], M = pm Bsin, - pm B. ()

= - pm B, = - pm Bcos. pm L ( )

, , mL

pm2Q

= , Q -

; m - . F = Q[vB], F=QvBsin,

8

v - ; - v B. : ) = BScos =Bn S, S - ; - : )

=S

ndSB

( ). ( ) = N. N .

= I .

dtd

i

= .

, v , U = Blvsin, l - ; - v B. , , ,

Q = /R, Q = N/R = /R, R - . L = /I.

dtdILs = .

L = 0 n2 V, n - ; V - . , R L:

)

=

LRt

eR

I 1 ( ), - ; t - ,

;

) LRt

eII

= 0 ( ), I0 - t=0; t - , .

2

2LIW = .

( ) w = BH/2, w=B2/(20), w = 0H2/2, B - ; H - .

9

1. L=80 I=50. , , , =0 . . -- . -- dB, Id1. , d . ():

=l

BdB ,rr

(1)

l , . -- :

[ ],4 3

0 rldrIBd r

rr

=

d - , dl I , - ; 0 - ; - , . ( , , , , ). , d (. 1), (1) : =

l

dBB ,

,sin4 2

0 dlr

IdB

=

-- Idl - . ,

,sin4 2

0 =l

dlr

IdB

(2)

, - . dl d :

sin/rddl = (. 1).

dlr 2

sin

r

drdr

=sin

sin2 . , r

, (=/sin ); ,

.sin

0

d

rrd

=

, (2)

10

,sin4

2

10

0 =

drI

B

1 2 - . :

( ),coscos4 210

0

=rI

B (3)

, 21 coscos = . (3)

,cos2 10

0

rI

B = (4)

. 1 ( ) 220202

142/

2/coslr

l

rl

l

+=

+= .

1cos (4),

2200

0

42 lr

lrI

B+

= . (5)

(5), =26,7 . , , ( ). ( . 2) . (. 1) . 2. D , I=60, d=10 . , (. 3),

1=5 , - r2= 12 . . B . 1 2 , , :

11

B = B1 + B2

: ,cos2 21

22

21 BBBBB ++= (1)

- 1 2. 1 2 1 1 r2 :

( ) ( )202101 2 ;2/ rI/BrIB == . 1 B2 (1) ( ) 2/0I ,

cos

2112 21

22

21

0

rrrrI

B ++= . (2)

cos . , DAC= ( ),

cos2 212

22

12 rrrrd += ,

d - .

4023

125210-12+5=cos ;

2cos

222

21

222

21 =

+

= rr

drr .

(2) :

( ) ( )

4023

12,005,02

12,01

05,01

14,32601014,34

22

7

++

=

B =3,0810-4= =308.

3. R=10 I=80. A, r=20 . . --:

[ ],4 3

0

rrldIBdrrr

=

d - , Idl , - . dl A - (.4). d . , :

=l

BdB ,rr

dl . d : dB, , dB||, , .. dB = dB + dB||

12

+=

l l

BdBdB ||rrr

, =l

Bd 0||r

d

dl , () : =

l

dBB ,

dB = dBcos ,4 20

rIdl

dB

=

( dl r , , sin = 1).

, .4

2coscos4 2

02

02

0

rRIdl

rIdB

R

==

2 cos R/r (. 4)

3

20

2rIR

B

=

, (): [ ][ ][ ]

[ ] . 11111

111

1111

1111

222

2

3

2

3

20

rRI

=

=

=

=

=

:

.maxp

MB = 211

11 1

=

: ( )

( ),1028,6

2,021,080104 5

3

27

B

=

=

= 62,8 .

( .4) . 4. I=50 =2/3.

(. 5). d=5 . . , (.6). - A 1 2 , 1 2, . . =1+2. 2 . --, , , d = 0 ([dlr] = 0).

13

B1 , (3),

1: ( ),coscos4 210

01

=

rIB

r0 - 1 (. 6). 10 ( ), 2 = .= 2/3 (s2 = s(2/3) = -1/2). r0 = dsin(-) = dsin(/3) = 2/3d .

( )2/112/34

01 += d

IB

.

B = B1 (B2 = 0), dI

B

43 0=

1, . . 6 ( , ). 3. :

.6,341046,31054

501043 52

7

B ==

=

5. (. 7). I1=80 I2=60. d 10. , . . B , I1 I2 , B=B1 +B2 , B1 - , I1 ; B2 - , I2 . , B1 B2 ( . 8). B : ,2212 BBBB +== B1 B2

: .2

2 0

202

0

101 r

IBrIB

== r0 = d/2.

.II 2221

0 +=d

B

3. :

. 400104608010104 422

1

7

==+

=

B

14

6. , . 9. R 10. , I = 80, . . , : B = Bi. (. 10): (1 3), , (2) R.

= 1 + 2 + 3, 1, 2 3 - , , , .

1, 1 = 0 = 2 + 3, , 2 B3 , : = 2 + 3, B2 , :

,2

0

RI

B

=

O ,

,4

02 R

IB

=

B3 , (3), 1:

( ),coscos4 210

0

=rI

B

r0 =R, 1 = /2 (cos1 =0), 2 (cos2 = -1)

.4

03 R

IB

=

2 3,

,44

0032 R

IRI

BBB

+=+=

15

( ).14

0 +=

RI

B

3. :

( ) ,1031,3 11,0480104 47 B

=+

=

B = 331 . 7. l = 2,5 , d=20 , 1= 1 A. . . , , . , . , ( I1 I2) . I1 ( I2) . ( . 11) - 1. 1

.2

01 d

IB

= (1)

, I2 dl ( ).sin12 BdldlBIdF = dl 1,

( ) 1sin =Bdl .12 dlBIdF =

1 (1),

.2

210 dldIIdF

=

F :

.22

210

0

210 ldII

dldII

Fl

==

, I1 = I2 = I, .2

20

dlI

F

=

, ():: [ ][ ][ ]

[ ]( )

.11

11

111 220

dlI

==

=

: ( ) .5,22,02

5,210104 237 HHF =

=

16

F dF (. 11) ( ) . 8. , U = 600 , = 0,3 . R . . , v. v, () n.

, F = man (1) - . . 12 () v. v ( n F ). , ( ). (1) ( ): F = man, (2) F = QvBsin. vB sin=1, F= QvB. n=v2/R, (2) : QvB = mv2/R. : R = mv/(QB). , mv (), R = p/(QB). (3) , , .. = , Q(1 - 2) = T1 - T2, 1 - 2 - ( U), T1 T2 - . (T1 0) T2 , QU = p2/(2m). Ump Q2= (3):

,Q

Q2B

UmR =

Q

2mU1B

R = .

, ():

17

[ ][ ][ ][ ]

( ) ( )

( )( )

( )( )

.1 1 1

11 1

11 1 11

111

11

Q

21

221

21

221

2122121

21

2121

BUm

=

=

=

=

=

=

(4) :

11,8= 0118,0106,1

6001067,123,0

119

27

=

=

R

9. , (=0,2 ), R=5. m . . , . . 13 ( ). ,

,Te

I =

e - ; T - . v , T= v/(2R). I=ev/(2R) (1) I, . ,

pm =I S, (2) S - , ,

(S=R2). I (1) (2),

.2

2RR

epm

=

R :

.ve21

m Rp = (3)

, R , , R=mv/(QB) (. 8). Q e, v=eBR/m (3)

18

.2

22

mRe

pmB

=

, (A2): [ ][ ][ ]

[ ]( ) ( ) ( )

=

=

=m 1 1 1 1

11 1K 1R B e 22222 ( ) . 1

1 1 2

2

222

=

: ( ) ( ) . 7,03= 1003,7

101,9205,02,0106,1 22122

31

2219

Apm =

=

10. (B=10)

, R 1 h=6. T v. . , (/2) . , .14, v : B (v||) (v). v|| .

v (Fv) ( (v|| = 0) , ). , : v|| v . -

T=2R/v (1) R/v. , an = v2/R F =ma n , ev B= mv2 /R, (2) v = v sin. (2) v, R/v= m/(eB) (1):

.2Be

mT =

, (c):

[ ][ ][ ] .1 1 1

1 1

1 1

B 2222

em

=

=

=

=

:

19

. 3,57=c 103,57=c 1010106,1

101,92 9319

31

=

T

v, . 14, v v|| : : 2||

2 vvv += (2) :

.vmBRe

=

v|| . , T, -, , .. h = Tv|| , v|| =h / T| T (2),

.2

v|| mBhe

=

,

.2

vvv2

22||

2

+=+=

hRmBe

, (/). , R h - (). (, R): [ ][ ][ ] [ ] ( ) =

=

=

= 1 1 1

1 1 1B

2

212212

Rm

e / 11 1

2 =

:

( ) =/206,001.0

101,91010101,6v

2122

31

319

+

=

2,46107 /c=24,6 /c.

11. - U = 104 (E=10 /) (B=0,1) . - , , , . . Q - m, :

,2vQ

2mU = .2v/Q

2

Um = (1)

v - . :

20

) F = Q[v], v ; ) F = Q, E (Q>0). . 15 Oz, v - Ox, F F , . - , F+F . Oy ( , vB sin = 1): QE-QvB=0, v = E/B. (1),

)./(2UBE = Q/m 22 , (/): [ ]

[ ][ ]( )

( )( )

( ) ( )/. 1

11

11

11 1

11 / 1

B 2222

2

2

2

2

=

=

=

=

=

UE

: ( )

( )/. 48,1=/ 1081,4/

1,0104210 7

2

24

=

= mQ

12. , N = 103 , n=10 c-1 AB, (B=0,04 ). , =60 . S 100 2. . - :

.dtd

i

= (1)

= N, N - , . (1),

.dtdNi = (2)

, t, =BScost, B - ; S - ; - . (2) , : .sin tNBSi = , n = 2n t = /2- (. 16), (, sin(/2 - ) = cos) .cos2 NBSi = , (B):

[ ][ ][ ] .11 1

11

11 1S B n

22

==

=

=

21

:

.1,255,01004,0101014,32 23 BBi ==

13. = 5 R = 10 (B = 40 ). = 30 . Q, , . . . ,

.dtd

i =

, RI ii /= ,

R - . .dtdRIi =

,dtdQIi =

.R

d-=dQ ,QdtdR

dtd

= (1)

(1),

.R-=Q ,1Q

0

211

2

=Q

dR

d

, ( ) 2=0,

Q =1/R (2) 1.

1 = BSs, S - . ( ) S = 2.

1 = Ba2s. (3) (3) (2),

.cosQ2

R

Ba=

, (): [ ][ ][ ]

( ) .11

11

11

11 222

RaB

==

=

=

:

. 67,81067,801,0

2/3102504,0Q 34

==

=

14. = 10 , I = 100 , (B =1 ). A,

22

, , : 1) 1 = 90; 2) 2 = 3. . . , (. 17) ,sinBpM m= (1) m = IS = I2 - ; - ; - m, ( ) .

. ( = 0), , = 0, . . m . , - [. (1)] . . ( ),

dA = Md. (1), dIBadA sin2=

, :

.sin0

2 =

dIBaA (2)

= 90

( ) .cossin2

0

22

022

1 ===

IBaIBadIBaA (3 )

(I = 100 A, = 1Tl, = 10 c = 0,1 ) (3):

. 1=(0,1)1100=A 21 2 = 3. , , 2 , (2) sin:

.212

0

22

222 ==

IBadIBaA

2 . (4)

( ) ( ) . 1,37= 101,37= 0523,01,0110021 322

2=A

:

23

1. , - :

( ),21 IIA == 1 - , ; 2 - , . 1 = 90, 1 = BS, 2 = 0. ,

,2IBaIBSA == (3). 2. ( ) .cos Bp m=

,12 A ==

( ).coscos 21 = BpA m m = I2, cos 1 = I cos 2 = 0, ,2IBaA = (3). 15. N = 1200 , . I = 4 = 6 . L W . . L 1 .LI= (1) , , N ( , ): .N= (2) (1) (2) : .INL = (3) .221 LIW = L (3), I21 NW = (3) (4) :

;8,1108,14

106102,1 363 L ===

W 4,14101,44= 4106102,121 263 ==

24

4

0 410 420 430 440 450 460 470 480 1 401 411 421 431 441 451 461 471 2 402 412 422 432 442 452 462 472 3 403 413 423 433 443 453 463 473 4 404 414 424 434 444 454 464 474 5 405 415 425 435 445 455 465 475 6 406 416 426 436 446 456 466 476 7 407 417 427 437 447 457 467 477 8 408 418 428 438 448 458 468 478 9 409 419 429 439 449 459 469 479

401. I = 50 , . ,

b = 20 . , . 402. I = 6A. a = 3 . B . 403. R=10 (.18). I, B A 1? =10. 404. , a = 8 b = 12 , I = 50 . H

405. . I1 = 100 I2=50. d = 20 . , 406. I = 100 . , , , . 19. R 20 . 407. I = 100 . , , , . 19. R 20 . 408. I = 100 . , , , . 19. R 20 .

25

409. I = 100 . , , , . 19. R 20 . 410. , , . 20 I =100. , r = 10 c. 411. , =10 , I= 100 . . F, L= 1 . 412. l = 3 I = 500 . d = 10 . F . 413. , R=10 , I=10 . F , , , , d 1. 414. =20 I= 10 . F , d 2 . 415. l = 40 , I=100, B=0,5. , , s= 40 , . 416. 500 / m = 6 2. I R .

26

417. R = 20 , I =50, H=103 /. = 0. 418. =4 b=1,5 , N=200 , =0,1 . . : 1) , , I=1; 2) pm . 419. S , 150 2, N=200 , I=4. =8/. pm , , , = 600 . 420. R=5 =2 /. =600 . I= 4. , . 421. R = 5 Q = 0,1 . , . n =20-1. : m , , (pm /L), m =100 . 422. l = 40 Q = 500 . = 20 / , . : 1) m, ; 2) (pm /L), m = 10 . 423. . pm L . . m L. 424. = 2 R = 4 . F . 425. . F, , B = 0,2 , R = 0,2 . 426. B = 4 R = 0,8 . ? 427. , v=2106 /, =0,52 . Q/m , R=4. , . 428. H=4/ v=10/.

27

. F, , R , . 429. , B=0,2, R=5. pm . 430. H=10/. . 431. - , , . R1 R2, - ? 432. , , . , m1 = 12 . . ., R1= 2 . m2 ( ) , R2 = 2,31 . 433. , , , . R1=5, - R2=2,5. m1/m2 , . 434. , U=2, =15,1 R=1. e/m v . 435. , U=600, =0,3 . R. 436. =0,1 E=100 /. , , . v . 437. , , U=800 , , (B=50 ) . E , . 438. v=100/ , (E=210 /) (B=3,3) . . , v . 439. (E=400/) (B = 0,2 ) . U, , , . (e/m) 9,64107/.

28

440. (B = 1 ) ( = 1 /). - v = 1 /. an - . 441. l=1 S=16 2 N=2000 I 10. 442. =20 , I=100 . , L=10 . , . 443. , S 25 2 , B=0,04 . , , = 300 . 444. 50 . l=50 . pm , . 445. d = 5 ( ) d=0,2. , I = 0,5 . 446. = 10 , I = 6 , = 0,8 =50 . A , ? 447. , I = 60, ( = 20 ). d = 10 . A , , , =/3? 448. , =10 , I=20, . = 200 (B=0,1). A, , . 449. , I=20 , B=0,016 . d 10. A, , = /2 , . , =2. 450. a=10, I=200 , (=0,2). , , , = 2/3. 451. ( = 0,1 ) n=5 -1 l = 50 , , . U.

29

452. L=40 v=5/ . U 0,6 . . 453. B=0,35 n=480 -1 , N=500 S=50 2. . max, . 454. B=1 L=20 , . R 0,1 . F, , v=2,5 /. 455. B 0,8 , N=100 S=400 2. n , Ei=200. 456. , , . Q = 50 . , r = 10 . 457. m = 5 . (=0,2 ) , . Q, , , . 458. r=4 , R=0,01 , B=0,04. = 300 . Q , ? 459. = 10 . Q , ? R 1 . B 50. 460. r = 0,04 ( = 0,6 ). . S= 200 2. Q, : 1) 0 45; 2) 45 90. 461. l = 0,8 D = 4 d = 0,25 , . L . 462. S = 10 2 N = 1000 . B I = 5 0,1 . L . 463. , , N = 250 L1 = 36 . L2 = 100 , , . ?

30

464. , S 5 2, N=1200 . B I=2 0,01 . L . 465. L=50 S , 4 2, d=0,2 , ( ). L . 466. L = 0,03 I = 0.6 . t = 120 . , . 467. I = 0,1 1 . L 0.01 . . 468. I = 0,6 . , L = 5 . 469. N = 800 . ( ) S = 10 2. , B = 8 . , , t = 0,8 . 470. L 2 . =50 , , . , t, . I0=10A. 471. N=1000 . I 1 , 0,1. W . 472. L ( ) 0,1 . I W 100 ? 473. l = 0,6 S =10 2. , , = 0,1. W ? . 474. D ( ) 50 . N = 2000 S = 20 2. W I=5. . . 475. , N = 1000 , 0,2 . W , I, , 1 . . 476. , R = 20 , N = 500 , I = 1 . w .

31

477. I r = 5 w 1 /3? 478. n = 10 ( ). w I = 10 . , . 479. n = 10 . . I w 1 /3 480. n = 20 . I w 0,1 /3? , .

5.

v = c/n,

c - ; n - . L = nl, l - n.

= L1 - L2 .

=

2 ,

- .

= k (k = 0, 1, 2, )

= (2k +1)./2 . , ,

2sin2 1

22 = ind , 2

cos2 2

= idn ,

d - ; n - ; i1 - ; i2 - .

( ) 2/12 Rkrk = (k = 1, 2, 3, ), k - ; R - . kRrk = .

32

, ( ) ,

asin = (2k+1)/2 (k = 0, 1, 2, 3, ), a - ; k - . , ( ) , dsin = k (k=0, 1, 2, 3, ), d - .

R = / = kN, - ( + ), , ; N - . - 2dsin = k, - ( , , ); d - . tg B =n21 , B - , ; n21 - . I = I0 cos2, I0 - , ; I - ; - , , ( , ). : ) = d ( ), - ; d - , ; ) = []d ( ), [] - ; - .

( )20

v1 c

mm

= 2

0

1 =

mm ,

m0 - ; v - ; - , - , ( = v/c).

E = mc2, 2

02

20

11 =

=

EcmE ,

E0 =m0c2 - . E = E0 +T,

33

T - .

( ) 20 cmmT = ,

= 1

11

20 ET .

( )20

v/c-1

vmp = , 20 1

= cmp .

E2 = E02 + (pc)2. - Re = T4 , Re - () ; - - ; T - . m = b/T, m - , ; b - . = h, h - ; - . m = /c2 = h/(c), - ; - . p = mc = h/.

2v max2

maxmATAh +=+= ,

h - , ; - ; Tmax - .

0 =A/h, 0 = hc/A, 0 - , ; 0 - , ; h - ; - .

( ) cos10

==cm

h ,

2

sin2 20

cm

h== ,

- , ; - , ; m0 - .

cm

h

0

= ( = 2,436 ).

p = Ee (1+)/c = w(1 + ),

E - (); w - ; - .

34

1. S1 S2 ( = 0,8 ) . . (n = 1,33), . dmin ? . , ,

, . , . .

( ) ,21212 += k (1)

1 - ; 2 -

; k = 0, 1, 2, .... dmin k = 0. (1)

,212 = (2) 2 1. . 21 : ,211 ll =

( )[ ] ( ) ( ).1min212minmin12 +=+= ndndd llll 1 2 (2): ( ) ( ) ( ) ,21 21min21 =+ llll nd ( ) ,21min =nd ( )[ ].12min = nd : ( ) .21,1133,12

8,0min d =

=

2. = 0,6 . m ,

l, 10. . . , , , . . . , 1 2 (. 22)

.

35

, :

( ) ( ).2,...1,0,=k 212 += k (1) ( )2cos2 dn (/2). /2 , 1 . (1) ,

( ) ,2122cos2 2 +=+ kndk (2) n - (n = 1,5); dk - , , k; 2 - . , ; , 2 , cos2 =1. (2),

.2 kndk = (3) k- dk , k+m- - dk+m . (. 60), , m l, :

( ) .sin ldd kmk = + (4) (3) dk dk+m (4). , , sin = (- ),

( ).

22 ll nm

nkmk

=+

=

,

.10215,12

106,010 44

=

=

. : 1 = 206 265" 2,06 105". = 210-42,06105" = 41,2". 3. . d=2. , (2 = 0,7 ) (2 = 0,41 ) . . , , m :

( ) ,sin dm = (1) d - ; - ; - . sin 1, m d/, .. .d m (2) (2) , :

86,27,02 =m ( ); 88,441,02 =m ( ).

36

, , mmax = 2 mmax = 4. 4. , .

= 97 (. 23). n1, , . . , , , , tg = n21, n21 - () ().

. , tg = n2/n1.

, = /2 , , tg(/2) =

n2/n1, ( ) .2/2

1 tgn

n =

: ( ) .33,113,15,1

2/975,1

1 ===

tgn

5. N1, N2 , = 60. , - I0 : 1) N); 2) . k = 0,05.

. 1. , (. 24), : . .

37

( ). . () . () , . , - , ,

( ).10211 kII = , I0 , , I1 - :

( ) .12

12

0

0

1

0

kkII

II

=

= (1)

:

.1,205,01

2

1

0 =

=II

, 2,1 . 2. I1 N2 : . , . I2 , N2, ( ):

,cos212 II = - N2. ,

( ) .cos1 212 kII = , I0 I2 , :

( ) .cos1 210

1

0

kII

II

=

I0/I1 (1),

( ).

cos12

221

0

kII

=

: ( )

.86,860cos05,01

222

1

0 =

=II

, 8,86 . 6. . , I , .

38

. , 48,9 /. . , ( . 25) (I - I) , .

,l = (1) l - . , , , (II - II) .

.cos20 II = , ,2 =

( ) .sinI=I ,cos 20220 = II (2)

(2) (1) ,arcsin 0II=l

( ) ,arcsin 01 II=l :

. 169,48

785,0arcsin9,48

12

1 ===l

7. , v = 0,9 , - . . :

p = mv (1) , ,

20 1 = mm (2)

m - ; m0 - ; =v/c - , . (1) m (2) , v = c, :

( ).

v11 20

20 c

c

mcmp

=

= (3)

:

39

.106,51039,081,01

101,9 22831 p =

=

0 , . . = - 0. E = mc2 E0 = m0c2, , ,

20

220 1 cmcmT =

:11

12

20

=

cmT (4)

:

( ) ( ) .1006,1129,21018,8181,01

1103101,9 13142831 T ==

=

m0c2 = 0,51 , : T = 0,511,29 = 0,66 . 8. , T = 5. . . . , . .

= m2. (1)

.1 20 = mm (2) m (1) (2) ; , m0c2 = 0,

.1 20 = EE (3) (3) , ( ),1 2202 = EE

( ) .2022 EEE = (4) , ( ) .vv 2 pccmmccE === (4) ,20222 EcpE =

( ) ( ) ( )( ).11 00202 EEEEcEEcp +== : - 0 = . , + 0 = + 20,

( ) ( ).21 0ETTcp += : , . ,

40

( ) ( )==

+=

+=

c

ccETT

p 5,551,02552 0 .1093,2

103106,15,5 218

13

=

9. , , = 0,58 . () Re . . Re

- - ,4TRe =

(1) - -; T - . :

,0 Tb= (2) b - . (2) (1),

( ) .40bRe = (3) :

22724

7

38 / 4,35/ 1054,3/

108,51090,21067,5 ==

=

eR

10. vmax , : 1) 1 = 0,155 ; 2) - 2 =1 . . :

,maxTA += (1) - , ; - ; Tmax - .

, hc= (2) h - ; - ; - .

,2v20mT = (3)

= 1

1

120

ET (4)

, . , : 0 , (3), E0, (3) , (4). 1. (2):

,1028,11055,1

1031063,6 187

834

1

=

=

41

. 8106,11028,1

19

18

1 =

=

(8 ) (0,51 ). , (1) (3):

,2v2max01 mA +=

( ) .2v 01max mA= (5) , . (5) :

[ ][ ] /. 1 1

1 1

121222121

0

1 =

=

=

m

A

. (5),

( ) ./1008,1/1011,9

1075,01028,12v 6311818

max =

=

2. -:

,1099,110

1031063,6 1312

834

2 hc

=

==

. 24,11024,1106,11099,1 6

19

13

2 ==

=

( = 4,7 ) (2 = 1,24 ), , : Tmax = 2 = 1,24 . , (4).

( ) ( ).2 00 TETTE ++= , v = c Tmax = 2 ,

( ) ( ).2v 20220max ++= EEc :

( )./1085,2/

24,151,024,124,151,02

103v 88max c =++

=

11. = 90. 2=0,4 . 1 . . :

.2

sin2 20

cmh

= (1)

42

= 1 - 2 - ; h - ; m0 - ; c - ; - . (1): 1) , 1 - 2; 2) 1 2 1 2 , =hc/; 3) c.

.2

sin2 22012

cm

hchchc=

hc :

( ) ( ) ,2sin22sin2 20002

22

20

202

1

=

=E

Ecm

cm (2)

E0 = m0c2 - . (2) . E0 = 0,511 ,

( ) . 85,1290sin4,02511,0511,04,0

21 =

=

12. = 663 . = 0,6 . : 1) F, ; 2) . . 1. p S :: F =pS. (1)

p = Ee ( + 1)/c, (2) E - ; c - ; - . (2) (1),

F = EeS( + 1)/c. (3) EeS ,

F = e( + 1)/c (4) , , =1:

( ) 4 111036,0

8 =+= HF

2. n1 , , .. : e = n1, = hc/,

,1 hcne =

( ).1 hcn e= (5) :

.1021031063,6

1063,66,0 1181834

7

1

=

= ccn

43

5

0 510 520 530 540 550 560 570 580 1 501 511 521 531 541 551 561 571 2 502 512 522 532 542 552 562 572 3 503 513 523 533 543 553 563 573 4 504 514 524 534 544 554 564 574 5 505 515 525 535 545 555 565 575 6 506 516 526 536 546 556 566 576 7 507 517 527 537 547 557 567 577 8 508 518 528 538 548 558 568 578 9 509 519 529 539 549 559 569 579

501. 1 . 0,55 . 2,5 . 1 ? . 502. 0,3 . 2 . 0,6 . . . 503. = 30 , b = 1,5 . ( n=1,5 ) =20. , x =0,65 . 504. 5 . , 7 . . 505. , (0,75 ) ( 0,45 ) ? 506. (n = 1.33) 30. , ( = 0.6 )? 507. = 0.55 . , x=0,21 . . 508. 12,5 . 1,00 1,50 . .

44

509. . , 1,50; 1,63 1,70. 1. 0,5 . 510. . =0,5 . , n1=1.000292 , n2=1.000272. 511. 0,5 , 1,4 1,2 . . . 512. 6- 5- 0,5 , 1 . . 513. , 90 : ) 760 ; ) 440 ? 514. b = 2,5 , =2,5 . h ( n=1,5) , =600 , ? 515. d = 0,005 . 1=760 2= 440 . 516. 5- , 10 , 15 . 0,45 . 517. , 1 0,5 . , ? 518. . 212'. , . 519. , 0,3 . , 30 . 520. N=1000 d=10 . : 1) =30 ; 2) .

45

521. , , , 60, 10 % . 522. 1 , , . 20. ? 523. (n=1,5). , . 524. 1,5. , . 525. n - (=589,3 ) L=30 , 1 ? 526. , , . ? 527. , , , , . 528. , , , 3 , . 529. 20., 18. 0,06 3 / . 530. d = 0,86 = 0,59. . 531. 3 ? 532. 931/. , ? 533. 0,9 . , . 534. ( = 0,5 ). 20. 2,3510-27 . 535. , 1,78 ? 536. 1,55106 ? 537. 9,5105. , ?

46

538. 0,97, - . 0,5 . . ? 539. , 2,9108 / ? 540. 9820'. . 0,4 . 1,54. 541. , max =400. 542. , ( 1 =780 ) ( 2 =390 ) 543. 150 C. , 5 ? . 544. 1 4 , 27 . 23 . , . 0,5. 545. , 2000 1 , 1002. 0,8. 546. 152, 3, 1 100. : ) , 1 , ; ) . 547. , 10 , . 27 . 548. , , , 2, 13 27 . 0,6. 549. 2000 , 0,4. . 550. 450 . . 551. , - =0,5. . 552. , 307, 2105 /?

47

553. 21014 . . 554. 310. , 1,5 . . 555. 810 . , , (=100 ) ? 556. 1,2. , 400. . 557. , : ) - 2,4 10-2 ; ) 0,12. 558. = 300? , 2,1. ? 559. , , 0,4? 560. 0,4 . 2 . ? 561. , 1. ? 562. (=600 ) , , 0,1 . , 1 5 2. 563. 10 4 . 500 . , . 10 %. 564. 600 0,2. , 10-7 ? 565. 500 10 . , . 566. 21014 , 0,2 . , 0,3? 567. 52 2 , 6 . : ) ; ) .

48

568. 200 - , , , 20% . 5 . 569. J= 0.1 /2 30 0,7. , . 570. 500 , 0,1 . 1 2 10 . 571. , 60 40 . 572. . , 60 120 1,5 . , , . 573. 0,51 120 . , . 574. 0,25 90 . . 575. 0,5 90 . : ) ; ) . 576. , 1,02 . 577. . 578. , 2,04 , 1,02 . 579. 0,15 , 3 . , . 580. , , 0,19 . 6. ,

. ( )

L = nh/2 mnvnrn = nh/2, m - ; vn - n - ; rn - n - ; h - ; n -

49

(n = 1, 2, 3,). n - rn = a0 n2 , a0 - . En = Ei /n2 , Ei - . , ,

= h = En2 - En1 , 2

22

1

11nn

Ei

=

n1 n2 - , , .

= 2

22

1

111nn

R

- ; R - . .

= h/p, p - . T: ) p = m0v; Tmp 02= ;

) ( )20

v/c-1

vv mmp == ; ( )TTEc

p += 021 ,

m0 - ; m - ; v - ; - ; E0 - (E0 = m0 c2 ). : ) px x h/2 ( ), px - ; x - ; ) Et h/2, E - ; t - . . . ( ) A = Z + N, Z - ( ); N - .

dN = - Ndt, N = N0e-t , dN - , dt; N - , t; N0 - (t=0); - . , t,

N = N0 -N = N0 (1-e-t ). , t, , T1/2 ,

50

N = Nt.

T1/2 = ln2/ = 0,693/. , .. , e ,

= 1/. N , ,

N = mN /M, m - ; M - ; N - . a = A/m. m = Zmp + (A - Z)mn - m , Z - ( ); A - ( ); (A - Z) - ; mp - ; mn - ; m - . E = mc2 , m - ; - . E=931m, m - ...; 931 - (1 ... 931 ). . 0

dmdn 2/12/3

22

22

1)(

=h

,

dn() - , + d; m - . < F ( F - ). T = 0

( ) ( ),23 3222 mnF h= n - . .

( ),20kTEe =

E - ; 0 - . p - n -

( )[ ]1/exp0 = kTeUII , I0 - ; U - , p - n - . .

e

U FF 2112

= ,

F1 F2 - ; e - .

51

1. . . . :

( ),111 22212 nnRZ = (1) - ; R - ; Z - ( Z = 1 ); n1 - , ; n2 - , (n1 n2 - ).

. hc= , (1) h, :

( ).11 22212 nnRhcZ = Rhc Ei ,

( ).11 22212 nnZEi = : Ei = 13,6 (. . 1 ); Z=1; n1=2; n2=4:

. 25,21636,1341

2116,13 22

2 ==

=

2. , , U. : 1) U1 = 51 ; 2) U2 = 510 . . p

,ph= (1) h - . , T. ( ) ( ).

,2 0Tmp = (2) m0 - .

( ) ,/2 0 cTTEp += (3) E0 = m0c2 - . (1) (2) (3) :

,2 0Tm

h= (4)

52

( ).

/2 0 cTTEh+

= (5)

, U1=51 U2=510, , (4) (5) . , U,

.eUT = T1 = eU = 51 = 0,5110-4, 0 = m0c2 = 0,51. , (4). , 1 = 10-4m0c2. (4),

.2

10

102 0

2

20

40

cmh

cmm

h=

=

, h/m0c , .21021 =

= 2,43 (. . 1 ), .171243,21021 ==

T2 = eU2 = 510 = 0,51 , .. . (5). , T2 = 0,51 = m0c2, (5)

( ),

3/2 0202

02

0

2 cmh

ccmcmcm

h=

+=

.32 =

: . 40,1343,22 ==

3. T = 10 . , - . .

,h xpx (1) x - ( ); px - (); h - . , , , , . l, -

.2l=x

53

(1)

( ) ,2 hl xp

.2 xp hl (2) px px, .. pxpx. px .2mTpx = px mT2 ( l). ,

.22min mThl = (3) , . (3) :

[ ][ ][ ]( ) ( )

= 1 1 1

1 1 1 21

2121

=

=Tmh . 1=c 1

1 1

2122

. :

. 124,01024,110106,1101,92

1005,12 101913

34

min ==

=

l

4. .73 Li . ( ) , . m ( ) , ..

( ) ,np mmZAZmm += (1) Z - ( ); A - ( , ); m, mn, m - , . , , (1) , m . , , : ma = m + Zme,

.ea Zmmm = (2) (1) (2),

m =Zmp + (A - Z)mn - ma +Zme, ( ) ( ) .enep mmZAmmZm ++=

, mp + me = mH, mH - , ( ) .anH mmZAZmm += (3)

(3) (. . 13 15 ),

( )[ ] ... 04216,0... 1601,0700867,13700783,13 m =+=

,2 mcE = (4) - . 2 :

54

2 = 91016 2/2, 2 = E/m = 91016 /. , , 2 = 931/... (4)

( ). 931 mE = (5) (5),

. 2,39 04216,0931 == E . : A: = ma - A. , . m, (1). 5. - B105 , . H11 . , . . XAZ . - He42 ,

.11105

42 XHBHe

AZ++

, 4 + 10 = 1 + A, A = 13. , 2 + 5 = 1 + Z, Z = 6. , .136C :

.13611

105

42 CHBHe ++

Q ( ) ( )[ ].931Q CHBHe mmmm ++=

, - - . . . Z. - . , , . , , . (. . 13 ) ,

( ) ( ) . 06,4 00335,1300783,101294,1000260,4931Q =++=

55

6. A0

Mg27 m = 0,2 , A t = 6. T1/2 . . A dN , dt, :

.dtdNA = (1) - , N . dN/dt, :

,0teNN = (2)

N - , , t; N0 - , (t = 0); - . (2) :

.0teNdtdN = (3)

(1) (3) dN/dt, t:

.0teNA = (4)

A0 t=0: .00 NA = (5)

T1/2

( ) ./2ln 21T= (6) N0 , , NA :

,0 AA NMmNN == (7)

m - ; M - . (6) (7) (5) (4)

.2ln

210 ANTM

mA = (8)

.2ln 212ln

21

tT

AeNTMmA = (9)

, , T1/2 = 10 = 600 (. . 14 ), 1n2 = 0,693, t = 6 = 63,6103 = 2,16. 104:

; 13,5 1013,5 1002,6600693,0

1027102,0 1223

3

9

0 ==

=

A

. 3,811002,6600693,0

1027102,0 41016,2600

693,023

3

9

=

=

eA

7. F ( ), () T=0 . , .

56

. F, T=0,

( ) ( ),23 3222 mnF h= (1) h - ; m - . ,

,MNn A= (2) - ; NA - ; M - . n (1),

.32

322

2

=

MN

mA

F h

: ( ) ( ) . 4,71018,1

10641002,6109,814,33

101,921005,1 18

32

3

2332

31

234

==

=

F

8. t1=0 t2=10. ? . T

( ),20kTEe =

0 - ; E - . ,

( )

( ) .11

2exp

212

2

2

1

==

TTkE

ee

kTE

kTE

'

E = 1,1 , :

( ) .28,22831

2731

1038,121076,1exp 23

19

2

1 =

=

6

0 610 620 630 640 650 660 670 680 1 601 611 621 631 641 651 661 671 2 602 612 622 632 642 652 662 672 3 603 613 623 633 643 653 663 673 4 604 614 624 634 644 654 664 674 5 605 615 625 635 645 655 665 675 6 606 616 626 636 646 656 666 676 7 607 617 627 637 647 657 667 677 8 608 618 628 638 648 658 668 678 9 609 619 629 639 649 659 669 679

57

601. , . . 602. , . . 603. . 604. : ) ; ) , . 605. , , , 2: ) ; ) , . 606. , n - , . 607. , , . , . 608. 94,5 130,0 ? 609. 734 /? 610. 121,6 . . 611. 16,5 . ? 612. He+ Li++ . 613. . . 614. , 2. , . 615. , ? 616. , , 1,892 . . 617. . , , .

58

618. . , . - . 619. , , 10 . . 620. 435 ? 621. ? 622. ( ), . 623. . . 624. , .. , , . 625. 13,6 . . 626. , 100 50 ? 627. , . 628. , ? 629. . ? 630. , 511 . 631. x vx = 1 /. x: ) ; ) m = 10 -13 ; ) 0,1. 632. : ) , ; ) , 0,1 , . ). 633. 1 x ~ 10-5 . vx ? 634. 300. . 635. 10-7 . ? . 636. 810-17 . ?

59

637. , 10-6 , 10-6 . 638. 10-8 . ? 639. 10-6. 10-10 ? 640. =12. = 0,12 . 641. , 100 . 642. - 40 +100. 0,72 . 643. - 23 +27 . 0,74 ? 644. . , . 645. 3 1028 -3. . 646. , 0,72, 0 15 . ? 647. 0 10 2,3 . . 648. , - CaAs, 10 20 3 . 649. , - , , 5,2 300 400 . 650. - 0,4 . 250 350 ? 651. , , Al27. 652. : ) O16; ) - B11. 653. : ) - B11; ) , O16 .

60

654. B11. . 655. , Ne20 - C12, , Ne20, He4, C12 , : 8,03; 7,07 7,68 . 656. ( ) 5B11 10Ne20. 657. ( ) 14Si28 26Fe56. 658. ( ) 30Zn68 56Ba137. 659. ( ), 82Pb207 92U235. 660. ( ), 26Fe56 82Pb207. 661. 92U238 82Pb206. - - ? . 662. 87,5 % 20Ca45 ? 663. ? 664. 86Rn222 1 ? 665. , ? 666. , , 1 18,2 %. 667. 1 106 ? 138 . 668. 4 10-7 -1. 75 % ? 669. 3,71010 : ) 1 ; ) ? - 5,5 . . 670. . . , 1 1 . 671. : 1) n + 5B10 -> 3Li7 + 2He4; 2) p + 5B11 -> 3 2He4. 672. : 1) 1H2 + 1H3 -> 2He4 + n; 2) 2He4 + 7N14 -> 8O17 + p. 673. , : 3Li6 + 1H2 -> 2 2He4. . , .

61

674. , Ne20 - C12. Ne20, He4 C12 , 8,03; 7,07 7,68 . 675. U235 200 . : ) , 1 ; ) 29,3 /, 1 U235. 676. 15 , 30 %. . 677. , U235 200 , , 3107 , 4,19 /. 678. (x) : ) B10 (x, ) Be8; ) O17 (d, n) X; ) Na23 (p, x) Ne20; ) X (p, n) Ar37. 679. 5B10 , . , . 680. 11Na23 11Na24 15,3 . 30,6 ? .

62

1. ( )

g 9,81 /2

G 6,6710-11 3/(2 ) N 6,021023 -1 R 8,31 /() k 1,3810-23 /K (T0 =273 K, p0 =1,01105 )

V0 22,410-3 3 /

e 1,6010-19 c 3,00108 / -

5,6710-8 /(24 )

()

b1 2,9010-3

b2 1,310-5 /(3 5 )

h 6,6310-34 R 1,1107 -1 a 0,52910-10

2,4310-12

B 0,92710-23 A2

Ei 2,1810-18 (13,6 )

... 1,6610-27 0 8,8510-12 / 0 410-7 /

2.

6,37106 5,981024 6,95108 1,74106 7,331022

3,84108

1,491011

63

3.

, /3 , /3

2,7103 8,93103 3,5103 8,90103 6,02103 8,4103 9,80103 11,3103 19,75103 10,5103 7,85103 1,90103 0,92103 7,15103 0,53103 2,3103

4.

, /3

( 4 ) 1,00103 1,26103 0,8103 0,9103 13,6103 1,26103 0,8103

5. , / , / 72 500 40 22

6.

, , 3,010-10 1,910-10 2,310-10 2,710-10

7. 81 2,0 -

2,2 7,0

8. , , 5,510-8 4010-8 9,810-8 11010-8 1,710-8 1,610-8

64

9.

Ei , Ei , 2,1810-18 13,6 3,9410-18 24,6 1,2110-17 75,6 1,6610-18 10,4

10.

2,42 1,63 1,33 1,48 1,47 1,50

11.

, , 5,910-19 3,7 7,210-19 4,5 3,510-19 2,2 3,710-19 2,3 7,0410-19 4,4 7,710-19 4,8 1010-19 6,3 3,410-19 2,1 7,510-19 4,7 3,210-19 2,0 6,410-19 4,0

12. ( ) Ar Z

Ar Z Ar Z

N 14 7 Mn 55 25 Al 27 13 Cu 64 29 Ar 40 18 Mo 96 42 Ba 137 56 Na 23 11 V 60 23 Ne 20 10 H 1 1 Ni 59 28 W 184 74 Sn 119 50 He 4 2 Pt 195 78 Fe 56 26 Hg 201 80 Au 197 79 S 32 16 K 39 19 Ag 108 47 Ca 40 20 C 12 6 O 16 8 U 238 92 Mg 24 12 Cl 35 17

65

13.

, ...

, ...

0n1 1,00867 4Be7 7,01693 4Be9 9,01219 1H1 1,00783 5B10 10,01294 1H2 2,01410 5B11 11,00930 1H3 3,01605 2He3 3,01603 612 12,00000 2He4 4,00260 6C13 13,00335 6C14 14,00324 3Li6 6,01513 7N14 14,00307 3Li7 7,01601 8O16 15,99491 8O17 16,99913

14.

89Ac225 10 53J131 8 20Ca45 164 27Co60 5,3 12Mg27 10 84Po210 184 88Ra226 1620 86Rn222 3,8 38Sr90 27 15P32 14,3 58Ce144 285

15. m0 E0

... 0,00055 9,1110-31 0,511 8,1610-14 1,00728 1,67210-27 938 1,5010-10 1,00867 1,67510-27 939 1,5110-10 2,01355 3,3510-27 1876 3,0010-10 - 4,00149 6,6410-27 3733 5,9610-10 0 - 0,14498 2,4110-28 135 2,1610-11

. 2

.. 020827 29 1998 2000 ., 17. 30.10.2000 . . Times New Roman. 6084 1/16. . . . . . 3.7. . - . . 5.0. 500 . 117. . 169300, ., ., 13. . 169300, ., ., 13.

.