5.3 Solutions
305
5.18 σ =
ne
2
τ
m
n =
6.02 × 10
23
× 8.88 × 10
6
63.57
= 8.38 × 10
28 m
−3
σ =
8.38 × 10
28
× (1.6 × 10
−19 )
2
× 2.3 × 10
−14
9.11 × 10 −31
= 5.422 × 10
7
Ω
−1 m
−1
K = σ C WF T = (5.422 × 10
7 )(2.31 × 10
−8 )(300) = 376 Wm
−1 K
−2
5.19 (a) σ =
1
ρ
=
1
1.72 × 10 −8 = 5.8 × 10
7
Ω
−1 m
−1
(b) μ = R H σ = (0.55 × 10
−10 )(5.8 × 10
7 ) = 0.0032 m
2 V
−1 s
−1
(c) τ =
μm
e
=
(0.0032)(9.11 × 10
−31 )
1.6 × 10 −19
= 1.82 × 10
−14 s
(d) n =
σ
eμ
=
5.8 × 10
7
(1.6 × 10 −19 )(0.0032)
= 1.13 × 10
29 m
−3
5.20 (a) R H =
V H t
i B
=
(4.5 × 10
−6 )(2 × 10
−5 )
(1.5)(2)
= 0.3 × 10
−10 m
3 C
−1
(b) n =
1
R H e
=
1
(0.3 × 10 −10 )(1.6 × 10 −19 )
= 2.08 × 10
29 m
−3
5.21 Integrating n(E) dE from zero to E F :
13.6 × 10
27
E F
0
E
1/2 dE = 8.5 × 10
28
E
3/2
F = 9.375
Or E F = 4.445 eV
5.22 v =
2E
m
=
2 × 4.445 × 1.6 × 10 −19
9.11 × 10 −31
= 1.25 × 10
6 m/s
5.23 v F =
2E F
mc 2
1/2
c =
2 × 5.5
0.511 × 10 6
1/2
(3 × 10
8 ) = 1.39 × 10
6 m/s
Since each atom contributes one electron, the density of electrons is equal to
that of atoms.
n =
6.02 × 10
26
× 10.5 × 10
3
108
= 5.85 × 10
28 e/m
3
Each atom occupies approximately a volume d
3 . Therefore
d =
1
5.85 × 10 28
1/3
= 2.576 × 10
−10 m