Reactor Kinetics and Neutron Sources

Question 1

Which one of the following is a characteristic of subcritical multiplication?

Answer 1

The subcritical neutron level is directly proportional to the neutron source strength.

Question 2

A nuclear power plant has been operating at 100 percent power for 2 months when a reactor trip
occurs. Two months after the reactor trip, with all control rods still fully inserted, a stable count rate
of 20 cps is indicated on the source range nuclear instruments.
The majority of the source range count rate is being caused by the interaction of __________ with the
detector.

Answer 2

fission neutrons from subcritical multiplication

Question 3

The total neutron flux in a shutdown reactor is constant at 5.0 x 10^3 n/cm^2
-sec. If non-fission neutron
sources are supplying a constant flux of 1.0 x 10^2 n/cm^2
-sec, what is Keff?

Answer 3

0.98

Question 4

Reactor power was increased from 1.0 x 10^-9 percent to 1.0 x 10^-6 percent in 6 minutes. The average
startup rate was __________ decades per minute.

Answer 4

0.5

Question 5

Reactor power increases from 1.0 x 10^-8 percent to 5.0 x 10^-7 percent in two minutes. What was the
average startup rate during the power increase?

Answer 5

0.85 DPM

Question 6

During a reactor startup, reactor power increases from 1.0 x 10^-8 percent to 2.0 x 10^-8 percent in two
minutes. What was the average reactor period during the power increase?

Answer 6

173 seconds

Question 7

During a reactor startup, reactor power increases from 3.0 x 10^-6 percent to 5.0 x 10^-6 percent in two
minutes. What was the average reactor period during the power increase?

Answer 7

235 seconds

Question 8

A small amount of positive reactivity is added to a reactor that is critical in the source range. The
amount of reactivity added is much less than the effective delayed neutron fraction.
Which one of the following will have the most significant effect on the magnitude of the stable reactor
period achieved for this reactivity addition while the reactor is in the source range?

Answer 8

Effective delayed neutron precursor decay constant

Question 9

A nuclear power plant is operating at steady-state 50 percent power in the middle of a fuel cycle.
Which one of the following will initially produce a positive startup rate?

Answer 9

Increase in main turbine load.

Question 10

The magnitude of the stable startup rate achieved for a given positive reactivity addition to a critical
reactor is dependent on the __________ and __________.

Answer 10

effective delayed neutron precursor decay constant; effective delayed neutron fraction

Question 11

A reactor is critical at 1.0 x 10^-8 percent power during a reactor startup. β�eff for this reactor is 0.0072.
Which one of the following is the approximate amount of positive reactivity that must be added to the
core by control rod withdrawal to attain a stable startup rate of 1.0 DPM?

Answer 11

0.2 %ΔK/K

Question 12

A reactor is being started for the first time following a refueling outage. Reactor Engineering has
determined that during the upcoming fuel cycle, β�eff will range from a maximum of 0.007 to a
minimum of 0.005.
Once the reactor becomes critical, control rods are withdrawn to increase reactivity by 0.1 %ΔK/K.
Assuming no other reactivity additions, what will the stable reactor period be for this reactor until the
point of adding heat is reached?

Answer 12

60 seconds

Question 13

Reactors A and B are identical except that the reactors are operating at different times in core life.
The reactor A effective delayed neutron fraction is 0.007, and the reactor B effective delayed neutron
fraction is 0.005. Both reactors are currently subcritical with neutron flux level stable in the source
range.
Given:
Reactor A Keff = 0.999
Reactor B Keff = 0.998
If positive 0.003 ΔK/K is suddenly added to each reactor, how will the resulting stable startup rates
(SUR) compare? (Consider only the reactor response while power is below the point of adding heat.)

Answer 13

Reactor A stable SUR will be greater.

Question 14

Given the following stable initial conditions for a reactor:
Power level = 1.0 x 10-8 percent
Keff = 0.999
Core β�eff = 0.006
What will the stable reactor period be following an addition of positive 0.15 %ΔK/K reactivity to the
reactor? (Assume the stable reactor period occurs before the reactor reaches the point of adding
heat.)

Answer 14

110 seconds

Question 15

Given the following stable initial conditions for a reactor:
Power level = 1.0 x 10^-8 percent
Keff = 0.999
Core β
� AEA
eff = 0.006
What will the stable startup rate be following an addition of positive 0.2 %ΔK/K reactivity to the
reactor? (Assume the stable startup rate occurs before the reactor reaches the point of adding heat.)

Answer 15

0.52 DPM

Question 16

A nuclear power plant has just completed a refueling outage and a reactor startup is in progress.
Reactor engineers have determined that during the upcoming fuel cycle, A EAβ�eff will range from a
minimum of 0.0052 to a maximum of 0.0064.
After the reactor becomes critical, control rods are withdrawn further to increase reactivity by an
additional 0.1 %ΔK/K. Assuming no other reactivity changes occur, what will the approximate
stable startup rate be for this reactor until the point of adding heat is reached?

Answer 16

0.5 DPM

Question 17

During a fuel cycle, plutonium isotopes are produced with delayed neutron fractions that are
__________ than the delayed neutron fractions for uranium isotopes, thereby causing reactor power
transients to be __________ near the end of a fuel cycle.

Answer 17

smaller; faster

Question 18

Following a reactor trip, when does the startup rate initially stabilize at –1/3 DPM?

Answer 18

When the short-lived delayed neutron precursors have decayed away.

Question 19

Delayed neutrons contribute more to reactor stability than prompt neutrons because they __________
the average neutron generation time and are born at a __________ kinetic energy.

Answer 19

increase; lower

Question 20

Which one of the following statements describes the effect of changes in the delayed neutron fraction
from the beginning of a fuel cycle (BOC) to the end of a fuel cycle (EOC)?

Answer 20

A given reactivity addition to an operating reactor at EOC results in a higher startup rate (SUR)
than at BOC.

Question 21

Delayed neutrons are important for reactor control because…

Answer 21

they greatly extend the average lifetime of each neutron generation.

Question 22

Two reactors are identical except that reactor A is near the end of a fuel cycle and reactor B is near the
beginning of a fuel cycle. Both reactors are operating at 100 percent power when a reactor trip occurs
at the same time on each reactor.
If no operator action is taken and the reactor systems for both reactors respond identically to the trip,
reactor A will attain a negative __________ second stable period; and reactor B will attain a negative
__________ second stable period.

Answer 22

80; 80

Question 23

Two reactors are identical except that reactor A is near the end of a fuel cycle and reactor B is near the
beginning of a fuel cycle. Both reactors are critical at 1.0 x 10-5 percent power.
If the same amount of positive reactivity is added to each reactor at the same time, the point of adding
heat will be reached first by reactor __________ because it has a __________ effective delayed
neutron fraction.

Answer 23

A; smaller

Question 24

Two reactors are identical except that reactor A is near the end of core life and reactor B is near the
beginning of core life. Both reactors are operating at 100 percent power when a reactor trip occurs at
the same time on each reactor.
If no operator action is taken and the reactor systems for both reactors respond identically to the trip, a
power level of 1.0 x 10-5 percent will be reached first by reactor __________ because it has the
__________ effective delayed neutron fraction

Answer 24

A; smaller

Question 25

Which one of the following is the reason that delayed neutrons are so effective at controlling the rate of
reactor power changes?

Answer 25

Delayed neutrons have a long mean generation time compared to prompt neutrons.

Question 26

Which one of the following distributions of fission percentages occurring in a reactor will result in the
largest effective delayed neutron fraction?

Answer 26

U-235 U-238 Pu-239

90% 7% 3%

Question 27

Which one of the following distributions of fission percentages occurring in a reactor will result in the
smallest effective delayed neutron fraction?

Answer 27

U-235 U-238 Pu-239

60% 6% 34%

Question 28

Two reactors are identical except that reactor A is near the beginning of core life and reactor B is near
the end of core life. Both reactors are critical at 10-5 percent power.
If the same amount of positive reactivity is added to each reactor at the same time, the point of adding
heat will be reached first by reactor __________ because it has a __________ effective delayed
neutron fraction.

Answer 28

B; smaller

Question 29

A nuclear power plant is operating at steady-state 50 percent power when a control rod is ejected from
the core. Which one of the following distributions of fission percentages in the core would result in
the highest startup rate? (Assume the reactivity worth of the ejected control rod is the same for each
distribution.)

Answer 29

U-235 U-238 Pu-239

60% 8% 32%

Question 30

Two reactors are identical except that reactor A is near the end of core life and reactor B is near the
beginning of core life. Both reactors are operating at 100 percent power when a reactor trip occurs at
the same time on each reactor. No operator action is taken and the reactor systems for both reactors
respond identically to the trip.
Ten minutes after the trip, the greater thermal neutron flux will exist in reactor __________ because it
has a __________ effective delayed neutron fraction.

Answer 30

B; larger

Question 31

Two reactors are identical except that reactor A is near the beginning of core life and reactor B is near
the end of core life. Both reactors are operating at 100 percent power when a reactor trip occurs at the
same time on each reactor. No operator action is taken and the reactor systems for both reactors
respond identically to the trip.
Ten minutes after the trip, the greater thermal neutron flux will exist in reactor __________ because it
has a __________ effective delayed neutron fraction

Answer 31

A; larger

Question 32

A step positive reactivity addition of 0.001 ΔK/K is made to a reactor with a stable neutron flux and an
initial Keff of 0.99. Consider the following two cases:
Case 1: The reactor is near the beginning of a fuel cycle.
Case 2: The reactor is near the end of a fuel cycle.
Assume the initial neutron flux is the same for each case.

Answer 32

The prompt jump will be greater for case 2, but the final stable neutron flux level will be the same
for both cases.

Question 33

A reactor is critical in the source range during the initial reactor startup immediately following a
refueling outage. The effective delayed neutron fraction is 0.0062. The operator adds positive
reactivity to establish a stable 0.5 DPM startup rate.
If the reactor had been near the end of a fuel cycle with an effective delayed neutron fraction of 0.005,
what would the approximate stable startup rate be after the addition of the same amount of positive
reactivity?

Answer 33

0.65 DPM

Question 34

The following data is given for the fuel in an operating reactor:
Nuclide        Delayed Neutron Fraction 
U-235                          0.0065
U-238                          0.0148
Pu-239                        0.0021
Fraction of Total fuel Composition
0.03
0.96
0.01
Fraction of Total Fission Rate
0.73
0.07
0.20
What is the delayed neutron fraction for this reactor?

Answer 34

0.0062

Question 35

The following data is given for the fuel in an operating reactor:
Nuclide        Delayed Neutron Fraction 
U-235                          0.0065
U-238                          0.0148
Pu-239                        0.0021
Fraction of Total fuel Composition
0.023
0.965
0.012
Fraction of Total Fission Rate
0.63
0.07
0.30
What is the delayed neutron fraction for this reactor?

Answer 35

0.0058

Question 36

Which characteristic of delayed neutrons is primarily responsible for enhancing the stability of a
reactor following a reactivity change?

Answer 36

They require more time to be produced following a fission event than prompt neutrons

Question 37

For an operating reactor, the effective delayed neutron fraction may differ from the delayed neutron
fraction because, compared to prompt neutrons, delayed neutrons…

Answer 37

are less likely to leak out of the reactor core, and are less likely to cause fast fission.

Question 38

Given the following data for a reactor:
• The average delayed neutron fraction is 0.0068.
• The effective delayed neutron fraction is 0.0065.
The above data indicates that this reactor is operating near the __________ of a fuel cycle; and a
typical delayed neutron is __________ likely than a typical prompt neutron to cause another fission in
this reactor.

Answer 38

beginning; less

Question 39

Initially, a reactor is critical at a stable power level well below the point of adding heat (POAH). When
considering the following 2 cases, assume the reactor remains below the POAH.
Case 1: A step addition of positive 1.0 x 10^-4 ΔK/K.
Case 2: A step addition of negative 1.0 x 10^-4 ΔK/K.
The time required for reactor power to change by a factor of 10 will be greater for case _____, because
delayed neutrons are more effective at slowing reactor power changes when reactor power is
__________.

Answer 39

2; decreasing

Question 40

Two identical reactors, A and B, are critical at 1.0 x 10-8 percent power near the beginning of a fuel
cycle. Simultaneously, positive 0.001 ΔK/K is added to reactor A, and negative 0.001 ΔK/K is added
to reactor B. One minute later, which reactor, if any, will have the shorter period and why?

Answer 40

Reactor A, because delayed neutrons are less effective at slowing down power changes when the
fission rate is increasing.

Question 41

The following data is given for the fuel in an operating reactor just prior to a refueling shutdown.
Nuclide Delayed Neutron Fraction
U-235 0.0065
U-238 0.0148
Pu-239 0.0021
Fraction of Total fission rate
0.64
0.07
0.29
During the refueling, one-third of the fuel assemblies were offloaded and replaced with new fuel
assemblies consisting of uranium having an average U-235 enrichment of 3.5 percent by weight.
Which one of the following describes how the above data will change as a result of completing the
refueling outage?

Answer 41

The fraction of the total fission rate attributed to U-235 will increase

Question 42

Which one of the following is the major cause for the change in the delayed neutron fraction from the
beginning to the end of a fuel cycle?

Answer 42

Changes in the fuel composition.

Question 43

Given the following data for the fuel in an operating reactor:
Nuclide        Delayed Neutron Fraction 
U-235                          0.0065
U-238                          0.0148
Pu-239                        0.0021
Pu-241                         0.0049
Cross Section for Thermal Fission
     531 barns
      < 1 barn
      743 barns
      1009 barns
Fraction of Total fission rate
0.58
0.06
0.32
0.04
What is the delayed neutron fraction for this reactor?

Answer 43

0.0055

Question 44

A nuclear reactor is operating at steady-state 100 percent power in the middle of a fuel cycle. Which
one of the following changes would cause the core effective delayed neutron fraction to increase?

Answer 44

The fast nonleakage factor decreases.

Question 45

Given the following data for a reactor:
• The average delayed neutron fraction is 0.0052.
• The effective delayed neutron fraction is 0.0054.
The above data indicates that the reactor is operating near the __________ of a fuel cycle, and that a
typical delayed neutron is __________ likely than a typical prompt neutron to cause another fission in
this reactor

Answer 45

end; more

Question 46

A reactor core has a delayed neutron importance factor of 1.02. If the average delayed neutron
fraction in the core is 0.0057, the effective delayed neutron fraction is…

Answer 46

greater than 0.0057.

Question 47

Which one of the following is the primary reason that delayed neutrons are more effective than prompt
neutrons at controlling the rate of reactor power changes?

Answer 47

Delayed neutrons have a longer mean generation time than prompt neutrons.

Question 48

Two identical reactors, A and B, with identical fuel compositions, are initially critical at
1.0 x 10^-8 percent power. Then, suddenly and simultaneously, positive 0.001 ΔK/K is added to
reactor A while negative 0.001 ΔK/K is added to reactor B.
One minute later, which reactor will have the shorter period, and why? (Note: λeff is the effective
delayed neutron precursor decay constant.)

Answer 48

Reactor A, because the value of λeff shifts toward the value of the decay constant for the
shorter-lived delayed neutron precursors when reactivity is positive

Question 49

A reactor is critical at a constant power level of 1.0 x 10-8 percent. Consider the following two cases:
Case 1: A step addition of positive 0.001 ΔK/K.
Case 2: A step addition of negative 0.001 ΔK/K.
Which case will produce the faster rate of power change one minute after the reactivity addition, and
why?

Answer 49

Case 1, because the effective delayed neutron precursor decay constant is larger during a power
increase.

Question 50

Which one of the following describes a condition in which a reactor is prompt critical?

Answer 50

The net positive reactivity in the core is greater than or equal to the magnitude of the effective
delayed neutron fraction.

Question 51

A critical reactor will become prompt critical when the reactivity is equal to the…

Answer 51

effective delayed neutron fraction.

Question 52

A reactor is operating at 75 percent power with the following conditions:
Power defect = -0.0157 Δ/K/K
Shutdown margin = 0.0241 Δ/K/K
Effective delayed neutron fraction = 0.0058
Effective prompt neutron fraction = 0.9942
How much positive reactivity must be added to make the reactor prompt critical?

Answer 52

0.0058 ΔK/K

Question 53

A reactor with a xenon-free core is critical several decades below the point of adding heat (POAH).
The operator continuously withdraws control rods until a positive 0.5 DPM startup rate (SUR) is
reached and then stops control rod motion.
When rod motion is stopped, the SUR will immediately… (Ignore any reactivity effects from fission
product poisons.)

Answer 53

decrease, and then stabilize at a value less than 0.5 DPM until power reaches the POAH.

Question 54

Positive reactivity is continuously added to a critical reactor. Which one of the following values of
Keff will first result in a prompt critical reactor?

Answer 54

1.01

Question 55

A reactor initially has a stable positive 1.0 DPM startup rate with no control rod motion several
decades below the point of adding heat (POAH). Control rods are inserted until a positive 0.5 DPM
startup rate is attained and then stopped.
When rod insertion is stopped, startup rate will immediately…

Answer 55

increase, and then stabilize at a value greater than 0.5 DPM until power reaches the POAH

Question 56

A reactor was stable at 80 percent power when the operator withdrew a control rod continuously for 2
seconds. Which one of the following affects the amount of Aprompt jump@ increase in reactor power
for the control rod withdrawal?

Answer 56

The differential control rod worth

Question 57

A reactor is operating at steady-state 75 percent power with the following conditions:
Power defect = -0.0185 ΔK/K
Shutdown margin = -0.0227 ΔK/K
Effective delayed neutron fraction = 0.0061
Effective prompt neutron fraction = 0.9939
How much positive reactivity must be added to make the reactor prompt critical?

Answer 57

0.0061 ΔK/K

Question 58

Refer to the partially labeled reactor response curve shown below for a reactor that was initially stable
in the source range. Both axes have linear scales. A small amount of positive reactivity was added
at time = 0 sec.
The response curve shows __________ versus time for a reactor that was initially __________

Answer 58

reactor fission rate; subcritical

Question 59

Two reactors are critical at the same power level well below the point of adding heat. The reactors are
identical except that reactor A is near the beginning of a fuel cycle (BOC) and reactor B is near the end
of a fuel cycle (EOC).
If a step addition of positive 0.001 ΔK/K is added to each reactor, the size of the prompt jump in power
level observed in reactor B (EOC) will be __________ than in reactor A (BOC); and the stable startup
rate observed in reactor B (EOC) will be __________ than in reactor A (BOC). (Assume the power
level in each reactor remains below the point of adding heat.)

Answer 59

larger; larger

Question 60

Refer to the partially labeled reactor response curve shown below for a reactor that was initially
subcritical in the source range and remained below the point of adding heat. A small amount of
positive reactivity was added at time = 0 sec.
The response curve shows __________ versus time for a reactor that is currently (at time = 60 sec)
__________.

Answer 60

reactor fission rate; supercritical

Question 61

A reactor is operating at equilibrium 75 percent power with the following conditions:
Total power defect = -0.0176 ΔK/K
Shutdown margin = -0.0234 ΔK/K
Effective delayed neutron fraction = 0.0067
Effective prompt neutron fraction = 0.9933
How much positive reactivity must be added to make the reactor prompt critical?

Answer 61

0.0067 ΔK/K

Question 62

Which one of the following is a characteristic of a neutron source installed in a reactor?

Answer 62

Provides a neutron level that is detectable on the source range nuclear instrumentation

Question 63

Neutron sources are installed in a reactor for which one of the following reasons?

Answer 63

To augment the shutdown neutron flux to allow detection on nuclear instrumentation

Question 64

Which one of the following neutron reactions yields the highest neutron production rate immediately
following a reactor trip from extended power operations during the tenth fuel cycle? (Ignore any
contribution from an installed neutron source.)

Answer 64

Photo-neutron reactions

Question 65

Which one of the following neutron sources undergoes the most significant source strength reduction
during the hour immediately following a reactor trip from steady-state 100 percent power?

Answer 65

Photo-neutron reactions

Question 66

Which one of the following is the neutron source that produces the greatest neutron flux for the first
few days following a reactor trip from extended high power operations?

Answer 66

Photo-neutron reactions in the moderator.

Question 67

Which one of the following describes the purpose of a neutron source that is installed in a reactor
during refueling for the third fuel cycle?

Answer 67

Ensures shutdown neutron level is large enough to be detected by nuclear instrumentation.