1000 Solved Problems in Modern Physics

8.3 Solutions 481

Fig. 8.14

The net current,

J=−

λtr

3

∂φ

∂x

=A 2 K

λtr

3

e−kx

Asx→ 0 ,J=

Q

2

=A 2 K

λtr

3

whenceA 2 =

3 Q

2 Kλtr

The complete solution is

φ=

3 Q

2 Kλtr

e−Kx (7)

8.89 Thermal diffusion time is given by

t=

λa

v

=

1

vΣa

NowΣa=σa

N 0 ρ

A

=

0. 003 × 10 −^24 × 6. 02 × 1023 × 1. 62

12

= 2. 44 × 10 −^3 cm−^1

t=

1

2. 2 × 103 × 2. 44 × 10 −^3

= 0 .19 s

8.90 The generation time for neutrons in a critical reactor is calculated from the
formula

t=

1

Σa<v>(1+L^2 B^2 )

=

1

0. 0006 × 2. 2 × 105 (1+ 870 × 0 .0003)

= 6 × 10 −^3 s

8.91 LetNbe the number of boron atoms/cm^3. Ignore the scattering of neutrons
in boron.