8.3 Solutions
481
Fig. 8.14
The net current,
J = −
λ tr
3
∂φ
∂ x
= A 2 K
λ tr
3
e
−kx
As x → 0, J =
Q
2
= A 2 K
λ tr
3
whence A 2 =
3Q
2K λ tr
The complete solution is
φ =
3Q
2K λ tr
e
−K x
(7)
8.89 Thermal diffusion time is given by
t =
λ a
v
=
1
vΣ a
Now Σ a = σ a
N 0 ρ
A
=
0.003 × 10
−24
× 6.02 × 10
23
× 1.62
12
= 2.44 × 10
−3 cm
−1
t =
1
2.2 × 10 3 × 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
Σ a < v > (1 + L 2 B 2 )
=
1
0.0006 × 2.2 × 10 5 (1 + 870 × 0.0003)
= 6 × 10
−3 s
8.91 Let N be the number of boron atoms/cm
3 . Ignore the scattering of neutrons
in boron.
481
Fig. 8.14
The net current,
J = −
λ tr
3
∂φ
∂ x
= A 2 K
λ tr
3
e
−kx
As x → 0, J =
Q
2
= A 2 K
λ tr
3
whence A 2 =
3Q
2K λ tr
The complete solution is
φ =
3Q
2K λ tr
e
−K x
(7)
8.89 Thermal diffusion time is given by
t =
λ a
v
=
1
vΣ a
Now Σ a = σ a
N 0 ρ
A
=
0.003 × 10
−24
× 6.02 × 10
23
× 1.62
12
= 2.44 × 10
−3 cm
−1
t =
1
2.2 × 10 3 × 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
Σ a < v > (1 + L 2 B 2 )
=
1
0.0006 × 2.2 × 10 5 (1 + 870 × 0.0003)
= 6 × 10
−3 s
8.91 Let N be the number of boron atoms/cm
3 . Ignore the scattering of neutrons
in boron.