Biomedical Engineering Reference
In-Depth Information
Tab l e 9 . 5
Average Distribution of Energy Among Products
Released by Fission of
235
U
Kinetic energy of charged fission fragments
162 MeV
Fission neutrons
6
Fission gamma rays
6
Subsequent beta decay
5
Subsequent gamma decay
5
Neutrinos
11
Total
195 MeV
10
-14
s) from the fission fragments,
while the other (delayed) neutrons are emitted later (up to
∼
the fission neutrons are emitted promptly (in
∼
1
minormore).The
delayed neutrons play an important role in the ease of control of a nuclear reactor,
as discussed in the next section.
9.11
Criticality
An assembly of fissionable material is said to be critical when, on the average,
exactly one of the several neutrons emitted in the fission process causes another
nucleus to fission. The power output of the assembly is then constant. The other
fission neutrons are either absorbed without fission or else escape from the sys-
tem. Criticality thus depends upon geometrical factors as well as the distribution
and kinds of the material present. If an average of more than one fission neutron
produces fission of another nucleus, then the assembly is said to be supercritical,
and the power output increases. If less than one fission occurs per fission neutron
produced, the unit is subcritical.
Criticality is determined by the extent of neutron multiplication as successive
generations are produced. If
N
i
thermal neutrons are present in a system, their ab-
sorption will result in a certain number
N
i
+1
of next-generation thermal neutrons.
The effective multiplication factor is defined as
N
i
+1
N
i
k
eff
=
.
(9.39)
The system is critical if
k
eff
=
1
, exactly; supercritical if
k
eff
>1
; and subcritical if
k
eff
<1
.
It is useful to discuss
k
eff
independently of the size and shape of an assembly.
Therefore, we introduce the infinite multiplication factor,
k
∞
, for a system that is
infinite in extent. For a finite system one can then write
k
eff
=
Lk
∞
,
(9.40)
where
L
is the probability that a neutron will not escape. The value of
k
∞
will de-
pend on several factors, as we now describe for uranium fuel.
