Мартыненко Т.П. и др. Практический курс физики. Квантовая физика. Элементы физики твёрдого тела и ядерной физики
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21
2) – = 10
–10
=12,4 , = 6,62·10
–24
· / , m = 2,21·10
–32
3) – – =10
–12
= 1,24 ,
= 6,62·10
–22
· / , m
= 2,21·10
–30
1.12.
?
0
= m
0e
·
2
,
m
0
= 9,1·10
–31
; = 3·10
8
/ .
λ
=ν=ε
hc
h .
e0
ε
=
ε
,
2
e0
cm
hc
⋅=
λ
,
,
4,2104,2
103101,9
1062,6
cm
h
12
831
34
e0
=⋅=
⋅⋅⋅
⋅
=
⋅
=λ
−
−
−
.
1.13.
= 1 ?
,
.
. 24,1/hc =λ=ε .
51,0cm
2
e0e0
==ε .
/hpp
e
ν== ,
42
e0
22
e
2
e
cmcp +=ε
(
)
42
e0
2
2
e
cmh +ν=ε
h ε=ν ,
42
e0
2
2
e
cm+ε=ε .
1
7,251,0/24,11//
2
e0e0e
>+=εε+=εε 1
2
.
.
,
2
e0
2
2
e0
e
11
cm
β−
ε
=
β−
=ε
:
2
0e
2
2
1
1
1
ε
ε
+=
β−
22
e0
2
/1
1
εε+
=β
22
22
e0
/εε
( )
(
)
2
C
2
2
2
e0
2
242
e0
2
2
e0
h
cm
hc
cm
λ
λ
=
λ
=
λ
=
ε
ε
cm/h
e0C
=
λ
– , 104,2
12−
⋅ .
,
( )
2
C
2
/1
1
λλ+
=β
( )
.c/108,2
/1
c
v
8
2
C
⋅=
λλ+
=
1.14.
.
/hp ν=
.
ν, ,
,
ν=
•
hnE
e
,
Sdt
dN
=n
•
–
, .
/hp ν= ,
/
h
ν
, –
/
h
2
ν
,
/
h
ν
/
h
ν
−
. ,
•
n , – n)1(
•
ρ− .
,
,
( ) ( ) ( )
ρ+=
ν
ρ+=
ν
ρ−+
ν
ρ
•••
1
c
E
c
h
n1
c
h
n1
c
h
n2
e
,
, , ,
( )
+1
c
E
=P
e
.
, w
e
= E
e
/c – ,
(
)
e
w1P
⋅
ρ
+
=
.
23
1.15.
( = 1).
= 0,6 . , .
S :
S
P
F
⋅
=
.
:
( )
+1
c
E
=P
e
,
– ; –
; – .
S, –
S = , – ,
( ) ( )
H10411
10
3
600
1
c
SPF
6
8
e
−
⋅=+
⋅
=ρ+
Φ
=⋅= .
1.16. ( = 0,662 )
= 0,8.
•
N ,
S =1
2
,
=1 .
•
n –
. S – , ,
,
( )
ρ−=
••
1SnN
.
•
n
:
ν=
•
hnE
e
,
–
( )
+1
c
E
=P
e
.
λ
=
ν
/
c
,
(
)
( )
116
c101,1
1
1
h
PS
N
−
•
⋅=
ρ+
ρ−
⋅
λ
= .
1.17.
,
J = 0,2 /
2
24
= 0,8, = 45º
S = 10
2
.
/
h
ν
.
ν
,
S ,
,
θ
⋅
⋅
=
cosSJ
e
,
J – .
,
, ,
•
N :
e
N ε⋅=
•
/N ε=
•
.
ν
θ⋅⋅
=
•
h
cosSJ
N
.
c
/
h
ν
,
(
)
θ
ν
cosc/h –
(
)
θ
ν
cosc/h2 ,
(
)
θ
ν
cosc/h
(
)
θ
ν
−
cosc/h .
,
•
N , – N)1(
•
ρ− .
,
,
( ) ( )
θ
ν
ρ+=θ
ν
ρ−+θ
ν
ρ=
•••
cos
c
h
N1cos
c
h
N1cos
c
h
N2
dt
dp
n
( )
θ⋅ρ+=
2
n
cosS
c
J
1
dt
dp
– dt/dp
n
, . .
( )
H106cosS
c
J
1
dt
dp
F
92
n
n
−
⋅=θ⋅⋅ρ+== .
1.18. ,
= 0,155 . = 4,7 .
25
(1.25) :
max
AT −ε= ,
λ=ε hc/ – , ,
– ;
max
T –
.
(1.27),
(1.28), , ,
. ,
:
0
,
(1.27),
0
, (1.28)
8hc/ =λ=ε . (8 )
51,0cm
2
e0e0
==ε . ,
max
T
2
vm
=T
2
maxe0
max
:
2
maxe0
A
2
vm
−ε= .
/101,1m/)(2v
6
0max
⋅=−ε=
.
1.19.
= 0,31 .
, ,
B76,1U
=
. .
(1.25)
max
TA
+
=
ε
.
Ue
⋅
max
UeT
⋅
=
.
UeA ⋅+=ε
UeA ⋅−ε=
, λ=ε hc/ ,
26
24,2Ue
hc
A =⋅−
λ
= .
1.20.
, = 3,74 .
(1.29)
332,01032,3
106,174,3
1031062,6
A
ch
7
19
834
0
=⋅=
⋅⋅
⋅⋅⋅
=
⋅
=λ
−
−
−
,
,
.
1.21. ,
,
,
. ,
.
.
.
ee0
ε
+
ε
′
=
ε
+
ε
e
p+p=p .
,
,
/p
ε
=
,
/p
ε
′
=
′
,
(
)
(
)
2
2
e0
2
e0
2
e
cc/pp ⋅ε+
′
−=ε+ε
′
−ε=ε .
,
,
2
22222
e
c)cos2p(cp ⋅θ
′
−
′
+=⋅
,
- .
42
e0
22
e
2
e
cmcp =−ε ,
2
00
242
e0
22
e
2
e
)(2)p(cmcp ε+ε
′
−−
′
−==−ε
27
(
)
(
)
0c/ppcos1pp
e0
=
′
−ε+θ−⋅ .
p ,
:
( )
2/sinp2cm
cmp
cos1pcm
cmp
p
2
e0
e0
e0
e0
θ⋅⋅+⋅
⋅
⋅
=
θ−⋅+⋅
⋅
⋅
=
′
.
cp ⋅=ε ,
:
( )
2/sin2cm
cm
cos1cm
cm
22
e0
2
e0
2
e0
2
e0
θ⋅ε⋅+⋅
⋅⋅ε
=
θ−⋅ε+⋅
⋅⋅ε
=ε
′
.
λ
=
ε
/hc
λ
′
=
ε
′
/hc ,
(
)
2/sin2cos1
2
θλ=θ−⋅λ=λ−λ
′
=λ∆
10·4,2
cm
h
12
e0
−
==λ – .
,
2
e0
cm ⋅<<ε ,
ε
′
=ε ,
λ
=
λ
′
,
.
1.22. ,
= 90º
e0
ε=ε . ?
e0e
T
ε
−
ε
=
.
ee0
ε+ε
′
=ε+ε ,
e0e
T ε
′
−ε=ε−ε=
,
2/sin2cm
cm
22
e0
2
e0
θ⋅ε⋅+⋅
⋅⋅ε
=ε
′
,
:
2/sin
cm
21
2/sin2
cm
T
2
2
e0
2
2
e0
2
θ
ε
+
θ
⋅
ε
= .
2
e0e0
cm ⋅=ε=ε , , = 90º,
255,0cm5,0T
2
e0
=⋅⋅= .
28
(
)
( )
/10
3
c
1/T
/T2/T
cv
8
2
e0
e0e0
==
+ε
ε
+
ε
= .
1.23.
.
2
e0
2
e
2
e
)c/(p)c/( ε=−ε
e0e
T
ε
−
ε
=
T/21
c
T
p
e0e
ε+=
,
e0
5,0T
ε
⋅
=
.
/·1032/cm5p
22
e0e
−
⋅=⋅⋅= .
1.24. 1.21 (
).
( . 1.3),
, :
ϕ⋅+θ⋅
′
= cospcospp
e
θ⋅
′
=ϕ⋅ sinpsinp
e
,
.
ϕ
′
+
θ
=
′
cos·p/pcosp/p
e
,
ϕθ=
′
sin/sinp/p
e
e
p/p
′
,
//
0e0e
1cmp1p/p εε+=+=
′
( . 1.21).
e0
/1
/2ctg
tg
εε+
θ
=ϕ .
°
=
θ
90
, =
0
2/1tg
=
ϕ
,
°
=
ϕ
25 .
29
1.25. ,
= 10 /
2
.
1.26. ,
, = 34 . ,
S = 6
2
.
1.27. W, t =1
S = 8
2
,
= 1,2 .
1.28. T = 10 .
,
S = 1
2
.
1.29. /
1%.
1.30.
,
.
1.31. , ,
.
= 32".
= 1,4 /(
2
· ). (
,
, r = 1,5·10
11
.)
1.32.
,
.
.
1.33.
= 600 = 0,8, : 1)
; 2) W,
S = 5
2
t = 10 .
1.34. S = 2
2
= 400 t = 5 W = 83 .
.
1.35. = 1 .
S = 25
2
= 2 . ,
30
, ,
?
1.36. , ,
= 280 .
,
= 325 /(
2
· ).
1.37. R = 10
= 1 .
,
= 0,25.
1.38.
m
(
,
)
max
t = 0º ?
1.39. = 5,3 .
,
m
,
(
,
)
max
.
1.40. ,
(
,
)
max
)
(
1
= 760 ); ) (
2
= 380 ).
1.41.
(
,
)
max
m
=580 . ,
, .
1.42.
(
,
)
max
1
= 2,4
2
=0,8 .
(
,
)
max
?
1.43.
m
,
(
,
)
max
, = 400 .
1
2
.
1.44.
(
,
)
max
= 4,16·10
11
/
3
.
m
?
1.45. = 2 .
: 1)
,
= 600 ; 2)