2.87. T — 2k (i
m AvN) m 0)2 — 0.37 kK.
2.88. v =
3kT 1n (m2/m1) =1.61 km/s.
M2 — 1
2.89. T = 113mv21k.
2.90. dN/N = (-7 2' ) 3/2 e-mv212hT 2nvl dvl dvx.
2akT
2.91. (vx)= 0, (I vx ) =1/. 2kT I nm•
2.92. (v1) = kT/m.
2.93. v =1/4r1 (v), where (v) = li8kT/am.
Co
2.94. p = 2mvx • vx dn (vx) = nkT ,
where
dn (vx) =
(m12nkT) 1/2n • e -m4/2hT dvx.
2.95. (1/v) =1/2mInkT = 4n (v).
2.96. dN/N= 21s (nkT)-3/2e-ena
dc; ep, =1/2kT; no.
2.97. SNIN = 3 6n e-3126i= 0.9%.
CO
2.90 — =
231
Q
AN
(nkT) 312 J
The principal contribution to the value of the integral is provided
by the smallest values of a, namely a x ao. The slowly varying factor
lii-can be taken from under the radical sign if ascribed the constant
value 1/- so. Then
AN 1 N = 2 V eolnkT e-sona
2.99. (a) vp,. = 1/3kT/m; (b) a pr = kT.
00
2.100. dv =
dn (42143-t)v cos 0 = n (2kT/am)I/2 sin 0 cos 0 de.
v=-0
n/2
2.101. dv =
dn (d52/4n) v cos 0 = n (m/2akT)3/2 e-mv2/211Tv3 dv.
e=o
2.102. F = (kT I Ah) ln = 0.9.10-0 N.
2.103. NA = (6RT Ind3Apgh) ln
6.4.1023 mo1-1.
2.104. 11/10 = ec.m2-m1vninT = 1.39.
2.105. h —
kT In (n21%)
(m2— mi) g •
2.106. Will not change.
2.107. (U) = kT. Does not depend.
2.108. w
riliT I M1 N 70 g.
2.109. M —
2RTp In 1
(P— Po) (r2— r?) 0)2 •
2.110. co = V (2RT M12) ln rl = 280 rad/s.
2.111. (a) dN = no e-ar2/hT4ar2 dr; (b)
kT/a; (c) dN =
= (a/akT)3/2 e -ar2/14T4TEr2 dr; (d) Will increase 13/2-fold.
1/ 8 e -e/kT de.