58.
(a) The average de Broglie wavelength is
λ
avg
=
h
p
avg
=
h
2mK
avg
=
h
2m(3kT /2)
=
hc
2(mc
2
)kT
=
1240 eV
·nm
3(4)(938 MeV)(8.62
× 10
−5
eV/K)(300 K)
=
7.3
× 10
−11
m = 73 pm .
(b) The average separation is
d
avg
=
1
3
√
n
=
1
3
p/kT
=
3
(1.38
× 10
−23
J/K)(300 K)
1.01
× 10
5
Pa
= 3.4 nm .
(c) Yes, since λ
avg
d
avg
.