p39 058

background image

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

.


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