5.3.1.
:
rn(n, T) = dEn,n+dn / dn.
n, n + dn :
an (n,T) = / .
, , . :
an (n,T) = 1. (5.3.1)
:
lm ×T = b, (5.3.2)
lm ( ), , , b , b = 2,898×10-3 ×.
-:
R (T) = sT 4, (5.3.3)
R (T) , s -, s = 5,67×10-8 /(2×4).
( ) , :
R (T) = ()sT 4.
() <1 , .
a (a < 1) . :
R (T) = asT 4. (5.3.4)
, , a = 0,21.
, :
= RS, (5.3.5)
S , R .
, S t,
Q = RSt. (5.3.6)
, (5.3.6) :
Q = asT4St. (5.3.7)
16. , 1 , 33, 18. 1,6 2.
: 1 = 18 = 291 ,
2 = 33 = 306 ,
S = 1,6 2.
t = 1 = 60 .
: DQ.
. , , (5.3.7) , a = 0,21:
Q = asT 4 St,
Q 1 = asT 14 St, Q 2 = asT 24 St.
:
DQ = Q 2 Q 1 = asT 24 St asT 14 St = 28,58 .
: Q = 28,58 .
17. 3,0 /2. , .
: R = 3,0 /2 = 30000 /2,
: lm.
. - (5.3.2) (5.3.3) . (5.3.3) (5.3.2):
|
|
R (T) = sT4 Þ = (R / s) 1/4;
lm ×T = b Þ lm = b/T = b/ (R / s) 1/4 = 3,4 .
: lm = 3,4 .
:
, (5.3.8)
.
qe Dj, :
= = qeDj, (5.3.9)
Dj = U (U ).
, , :
= A. (5.3.10)
V 0, p = mV 0, :
. (5.3.11)
18. 100 . , , . m = 9,1×10-31 .
: U = 100 ,
m = 9,1×10-31 ,
qe = 1,6×10-19 .
: l , , V.
. (5.3.8), (5.3.9) , Dj = U:
, = qeDj = qeU, (5.3.9):
p = , , (5.3.8):
= 1,23×10-10 .
: = qeU = 1,6×10-17 .
:
V = p/ m = / m = 5,93×106 /.
: l = 1,23×10-10 , = qeU = 1,6×10-17 , V = 5,93×106 /.
.
:
= hn = hc / l, (5.3.12)
h , n , c , l .
, N :
= N = N hn = N hc / l. (5.3.13)
:
= ×t, (5.3.14)
, t .
:
Z . (5.3.15)
:
A = 1/ d. (5.3.16)
: nsin (u /2).
19. , . , 640 , 14 . , 1 3,2×1017 ? , 0,01 ?
: l = 640 = 640×10-9 ,
= 14 = 14×10-3 ,
t = 1 ,
N 2 = 3,2×1017,
t 1 = 0,01 .
: N 1, , W.
. ) N 1 (5.3.13) (5.3.12):
= N 1 , = hn = hc / l,
= N 1 hn = N 1 hc / l Þ N 1 = × l / hc = 4,48×1016.
) (5.3.14): = ×t.
=N 2 hn = N 2 hc / l, (5.3.14)
= / t = N2hc /(lt) = 0,1 .
|
|
) (5.3.13) , 0,01 0,01 , :
W = 0,01 N 2 hn = 0,01 N 2 hc / l = 9,94×10-4 .
: N 1 = 4,48×1016, = 0,1 , W = 9,94×10-4 .
20. , , 0,21×10-16 , u = 10-2 .
: = 0,21×10-13 ,
u = 10-2 = 0,57.
: Z.
. , (5.3.15):
Z ,
, (, ) (5.3.8):
,
, , :
= = , p = ,
= 1,07×10-10 .
(5.3.15) :
Z = (n = 1 ) = 1,07×10-8 .
, (5.3.16):
A = 1/ d = 9,3×107 -1.
: nsin (u /2) = 4,97×10-3.
: d = 1,07×10-8 .
5.3.4.
:
hn = hc/l = gm, (5.3.17)
h , n , c , l , g , m = 9,27×10-24 ×2 , .
21. = 0,25 . , . 2.
: = 0,25 ,
g = 2.
: l.
. (5.3.17) :
hc / l = gm Þ l = hc / gm = 0,043 .
: l = 0,043 .
22. , 2/3 2. ?
: g 1 = 2/3,
g 2 = 2.
: l 2/ l 1.
. l2 l1, (5.3.17):
hc / l 1 = g 1 m Þ l 1 = hc /(g 1 m);
hc / l 2 = g 2 m Þ l 2 = hc /(g 2 m).
l 2/ l 1 = g 1/ g 2 = 0,333,
.
: .