4.5 Neutron Initiators
169
of the historical documentation refers to production rates per unit operating power
per unit mass of fuel. However, the mass of fuel involved is not the mass of
235 U
alone, but rather that of the entire mass of uranium within the reactor, the majority of
which will be
238 U. The total number of nuclei is given by this total mass of the fuel,
M fuel , divided by its atomic weight A U of natural uranium, multiplied by Avogadro’s
number N A . The number of
235 U nuclei is then the total number of nuclei times the
fractional abundance f (= 0.0072 for natural uranium) of
235 U. In fuel-mass form,
(4.35) becomes
=
P t A U
E f M f uel f N A σ f 5
.
(4.36)
On adopting A U = 0.23803 kg mol
−1 , E f = 180 meV, f = 0.0072, and σ f 5 =
585 b, this reduces to.
=
3.254 × 10
13 s
2 m
−4
P t
M f uel
.
(4.37)
This expression assumes MKS units: P t in Watts and M fuel in kg. However, in
Manhattan Project documents, fuel loads are usually quoted in US tons and power
outputs in megawatts (P MW ); also, in the reactor engineering community, neutron
fluxes are usually cited in number per square centimeter per second. In these units,
(4.37) becomes
=
3.587 × 10
12 ton MW
−1 cm
−2 s
−1
P MW
M f uel
.
(4.38)
In reality, the neutron flux within a reactor is a function of position, with the flux
decreasing from the center of the core to the edges. A complete treatment involves the
neutron diffusion equation, but a simple rate-equation-based calculation will suffice
for order-of-magnitude estimates.
The rate equation is now used a second time, in order to get the rate of production of polonium nuclei. Suppose that a mass M Bi of bismuth of atomic weight A Bi
and thermal-neutron capture cross-section σ Bi is introduced into the reactor. The
instantaneous rate of production of Po nuclei is then given by.
R Po =
M Bi N A
A Bi
σ Bi .
(4.39)
Here we have A Bi = 0.20898 kg mol
−1 , and the KAERI website referenced in
Appendix B gives σ Bi = 0.03384 b. These values give.
R Po =
3.173 × 10
8 s
−1 kg
−1
P MW M Bi
M f uel
.
(4.40)
169
of the historical documentation refers to production rates per unit operating power
per unit mass of fuel. However, the mass of fuel involved is not the mass of
235 U
alone, but rather that of the entire mass of uranium within the reactor, the majority of
which will be
238 U. The total number of nuclei is given by this total mass of the fuel,
M fuel , divided by its atomic weight A U of natural uranium, multiplied by Avogadro’s
number N A . The number of
235 U nuclei is then the total number of nuclei times the
fractional abundance f (= 0.0072 for natural uranium) of
235 U. In fuel-mass form,
(4.35) becomes
=
P t A U
E f M f uel f N A σ f 5
.
(4.36)
On adopting A U = 0.23803 kg mol
−1 , E f = 180 meV, f = 0.0072, and σ f 5 =
585 b, this reduces to.
=
3.254 × 10
13 s
2 m
−4
P t
M f uel
.
(4.37)
This expression assumes MKS units: P t in Watts and M fuel in kg. However, in
Manhattan Project documents, fuel loads are usually quoted in US tons and power
outputs in megawatts (P MW ); also, in the reactor engineering community, neutron
fluxes are usually cited in number per square centimeter per second. In these units,
(4.37) becomes
=
3.587 × 10
12 ton MW
−1 cm
−2 s
−1
P MW
M f uel
.
(4.38)
In reality, the neutron flux within a reactor is a function of position, with the flux
decreasing from the center of the core to the edges. A complete treatment involves the
neutron diffusion equation, but a simple rate-equation-based calculation will suffice
for order-of-magnitude estimates.
The rate equation is now used a second time, in order to get the rate of production of polonium nuclei. Suppose that a mass M Bi of bismuth of atomic weight A Bi
and thermal-neutron capture cross-section σ Bi is introduced into the reactor. The
instantaneous rate of production of Po nuclei is then given by.
R Po =
M Bi N A
A Bi
σ Bi .
(4.39)
Here we have A Bi = 0.20898 kg mol
−1 , and the KAERI website referenced in
Appendix B gives σ Bi = 0.03384 b. These values give.
R Po =
3.173 × 10
8 s
−1 kg
−1
P MW M Bi
M f uel
.
(4.40)