Мартыненко Т.П. и др. Практический курс физики. Квантовая физика. Элементы физики твёрдого тела и ядерной физики
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11
A
≥
ε
. A
=
ε
,
.
0
ν
0
λ
, ,
:
h
A
0
=ν ,
0
A
hc
=λ . (1.29)
. 1.2
.
U, ,
,
:
e
NeI
•
⋅= , (1.30)
e
N
•
- ,
, –
.
.
,
, . ,
( ) U .
,
max
TUe
=
⋅
,
2
vm
Ue
2
maxe0
=⋅ . (1. 31)
.
–
( ) ,
.
,
.
λ
−
λ
′
=
λ
∆
.
λ
∆
, .
, .
U
I
I
U
. 1.2
12
, ,
. ,
, .
p
:
ee0
ε
+
ε
′
=
ε
+
ε
, (1.32)
e
ppp
+
′
=
(1.33)
2
e0e0
cm=ε – ,
λ
=
ε
/hc
λ
=
/hp –
,
λ
′
=
ε
′
/hc
λ
′
=
′
/hp –
.
,
, . 1.3.
(1.32), (1.33) :
2
e0e0
2
22
e
)(22 ε+εε
′
−ε+ε
′
ε−ε
′
+ε=ε (1.34)
θ
′
−
′
+= cospp2ppp
2
22
e
. (1.35)
(1.35)
2
θε
′
ε−ε
′
+ε=θ
′
−
′
+= cos2coscpp2pcpcp
222
2
2222
e
2
c (1.36)
,
(1.18). (1.36) (1.34).
42
e0
22
e
2
e
cmcp =−ε (1.37)
(
)
(
)
e0
2
e0
42
e0
2cos12cm εε
′
−ε+ε+θ−ε
′
ε−=
)cos1()(
e0
θ−ε
′
ε=εε
′
−ε
, (
0
ε⋅ε
′
⋅ε ),
)cos1(
111
0
θ−
ε
=
ε
−
ε
′
, (1.38)
(1.38)
λ
=ε
hc
,
λ
′
=ε
′
hc
,
2
e0e0
cm=ε ,
)cos1(
θ
−
λ
=
λ
−
λ
′
=
λ
∆
2/sin2
2
θλ=λ∆ (1.39)
θ
ϕ
p
. 1.3
p
13
104,2
cm
h
12
e0
−
⋅==λ – .
. ,
, ,
, .
,
.
,
.
1.1. (1.10)
- - .
(1.10) (1.2) ,
kT
/
h
x
ν
=
,
h
/
kTdx
d
=
ν
,
h
/
kTx
=
ν
:
0
x
3
32
44
x
3
0
4
44
2
0
kT/h2
3
0
0
T
e
0
1e
dxx
hc
Tk2
1e
dxx
h
Tk
c
h2
d
1e
1
c
h2
dMM
−
π
=
−
⋅
π
=ν⋅
−
⋅
νπ
=ν=
ν
ν
15
1e
dxx
4
0
x
3
π
=
−
, :
44
32
454
32
44
e
0
TT
h
c
15
k2
15
h
c
Tk2
M ⋅σ=⋅
π
=
π
⋅
π
= ,
:
( )
(
)
( ) ( )
42
8
3
34
2
8
4
23
5
32
45
1067,5
1062,610315
1038,114,32
hc15
k2
⋅
⋅=
⋅⋅⋅⋅
⋅⋅⋅
=
π
=σ
−
−
−
.
, -
σ
.
1.2. ?
.
= 6000 .
r = 6,95·10
8
.
d
dS
dS·Md
0
ee
=Φ
0
e
M
– (1.12)
14
40
e
TM ⋅σ= , = 5,67·10
–8
/(
2
·
4
).
,
2
C
r4S ⋅π= :
0146,4Tr4S·M
2642
C
0
ee
⋅=⋅σ⋅⋅π==Φ
1.3. ,
, : )
( = 3000 ); ) ( = 6000 ); )
, = 10
7
?
.
(1.14),
:
T/b
m
=
λ
, b = 2,90·10
–3
·
, :
) 1097,0
10
3
109,2
T
b
6
3
3
m
−
−
⋅=
⋅
⋅
==λ ( );
) 1048,0
10
6
109,2
T
b
6
3
3
m
−
−
⋅=
⋅
⋅
==λ ( );
) 109,2
10
109,2
T
b
10
7
3
m
−
−
⋅=
⋅
==λ ( ).
1.4.
m
= 0,50 .
, ,
. r
= 6,95·10
8
,
r = 1,5·10
11
.
:
dSd=
d
– ,
dS r.
r .
,
r :
15
ee
S·E
=
Φ
,
2
r·4S π= , r – .
,
, r :
0
ee
S·M
C
=Φ ,
2
r4S π= , r – .
:
CC
ee
Φ
=
Φ
.
, ,
:
(
)
2
C
C
0
ee
r/rM=E .
- (1.12)
40
e
CC
TM ⋅σ= ,
– , = 5,67·10
–8
/(
2
·
4
),
,
, (1.14):
mC
/bT
λ
=
, b = 2,90·10
–3
· .
:
2
C
4
m
e
r
r
b
E
λ
⋅σ= .
, : = 1,4 /
2
.
1.5. 500P
=
.
5d
=
T = 700º .
α
?
2
e
1
e
P
Φ
+
Φ
=
, (1)
1
e
Φ
2
e
Φ
– ,
. P/
2
e
Φ
=
α
.
(1) :
16
P
1
P
P
11
ee
Φ
−=
Φ
−
=α (2)
,
SM
0
ee
1
⋅=Φ , (3)
0
e
M – ,
- ,
40
e
TM ⋅σ= ,
4/dS
2
π=
– .
(3)
α
(2)
:
8,0
P
T
4
d
1
42
=
σ
⋅
π
−=α .
1.6.
i
1
= 1
1
= 1000 .
2
= 5000 ?
,
1
,
2
, :
1
= 0,115;
2
= 0,334;
1
= 25,7·10
–8
· ,
1
= 96,2·10
–8
· .
.
e
P
Φ
=
,
– , ; – ,
. r – ; L – ; i –
; R – .
, ,
-
222
r/LiRiP πρ==
,
rL2M
ee
π
⋅
=
Φ
e
M – ,
0
e
M ,
(1.8)
0
eTe
MaM ⋅= ,
- (1.12)
40
e
TM ⋅σ=
, ,
,
rL2T·a
4
Te
π⋅σ=Φ .
17
:
(
)
324
1T1
2
1
r2TaTi
1
π⋅σ⋅=ρ⋅
(
)
324
2T2
2
2
r2TaTi
2
π⋅σ⋅=ρ⋅
2
i ,
( )
A9,7
a·)T(
a·)T(
T/Tii
1
2
T2
T1
2
1212
=
ρ
ρ
= .
1.7.
,
?
,
, 76,0
k
=
λ
,
– 38,0=λ .
, -
40
e
TM ⋅σ= .
,
m
λ
, (1.14)
m
/bT
λ
=
.
,
m
λ
:
(
)
4
m
0
e
/bM λ⋅σ= .
k
λ
λ :
(
)
( )
16n
TM
TM
n
4
4
4
k
k
0
e
0
e
==
λ
λ
== .
16 .
1.8.
,
.
. ,
: 1) , 2) .
18
, ,
1
,
2
, :
2e1e
Φ
=
Φ
1. , ,
:
S·E
e2e
=
Φ
,
S – , .
1
, -
40
e
TM ⋅σ= ,
:
·2STS2·M
40
e1e
σ==Φ ,
:
(
)
(
)
K3302/ES2/T
4/1
e
4/1
e
=σ=σΦ=
2. , ,
,
S·E·a
eT2e
=
Φ
.
1
:
S·2T·aS2·M·aS2·M
4
T
0
eTe1e
σ===Φ
,
= 330 .
1.9.
,
1,0
=
λ
∆
T = 3000 .
,
1
2
,
(1.2)
λ
λ
λ
λ=∆
2
1
dMM
Te
0
T
M
λ
, (1.11).
12
λ
−
λ
=
λ
∆
,
m
21
2
λ=
λ
+
λ
=λ ,
19
m
,
,
(1.14).
= 3000 .10
6
m
−
λ=λ
,
1
10
10
10
3
6
9
<<==
λ
λ∆
−
−
−
(
)
λ∆⋅λ∆
λ m
0
Te
MM ,
(
)
m
0
T
M λ
λ
(1.15). ,
25
e
/2,3·CTM ≈λ∆∆ .
1.10. d = 1,2
,
.
0
= 300 . , ,
n = 2,0 .
Q
. ,
,
.
, dt
t
dTmCdQ ⋅−= (1)
dT – ( ) ; –
; m – .
dW, dt. –
, dt
dtdW
e
⋅
Φ
=
, (2)
–
S
SM
0
e
0
e
⋅=Φ
. (3)
20
0
e
M - (1.12)
2
dS π=
– .
:
dW
dQ
=
. (4)
6/dV
3
π=
,
ρπ=
3
d
6
1
m (5)
(1) dTdC
6
1
dQ
3
ρπ−= . (6)
(2), (3) (1.12)
dTTddW
42
σπ=
(7)
(4) (6) (7),
, t .
:
dt
dC
6
T
dT
4
⋅ρ⋅
σ
⋅
= (8)
0
1
,
0
/
1
=n, t:
(
)
3n
T18
dC
t
3
3
0
−
⋅σ
⋅
ρ
= . (9)
: = 8,9·10
3
/
3
,
= 395 /( · ). , (10), :
d = 1,2·10
-2
,
0
= 300 , n = 2, = 5,67·10
-8
/(
2 2
).
, t = 3 .
1.11. , ,
:
1) –
6,0
=
λ
;
2)
0
A1=λ
;
3) -
0
A01,0=λ
.
: λ=ν=ε /hch , : //hp ε=ν= ,
:
22
c/c/hm ε=ν= .
λ
=
ν
/
c
, h = 6,62·10
-34
· ;
1) = 0,6·10
–6
, = 2,07 ,
= 1,1·10
–27
· / , m = 3,68·10
–36