Question 32: As core age increases, the reactor response to a given reactivity addition will become _____________ due to the buildup of isotopes that have a _____________ delayed neutron fraction.
a. quicker, smaller*
b. slower, smaller
c. quicker, larger
d. slower, larger
Comment: The asterisk indicates the intended correct answer is choice "a". The question is technically incorrect because of the ambiguous wording. What does "a given reactivity addition mean"? Is the "addition" positive or negative? It is not likely that the neutron response will be visibly faster for a step change in reactivity. Nor is the 80 second period following a scram likely to change. Restate the question as follows:
Question 32: (revised) As core age increases, the positive stable reactor period for a fixed (constant) incremental reactivity addition from criticality will become _____________ due to the buildup of isotopes that have a _________________ delayed neutron fraction.
a. shorter, smaller*
b. longer, smaller
c. shorter, larger
d. longer, larger
Question 34: Why do delayed neutrons have such a dominant effect upon reactor period?
a. short delayed neutron lifetime
b. long delayed neutron lifetime
c. short delayed neutron generation time
d. long delayed neutron generation time*
Comment: The asterisk indicates the intended correct answer is choice "d". The question is technically incorrect because the delayed neutrons do not have a "generation time" ... they do have a "mean lifetime" of 12.5 seconds at steady state. Choice "b" is closer to being correct than is Choice "d". For a given off-critical condition in the Delayed-Critical region, the only means for power change is by a changing delayed neutron source strength. It is the delayed neutron mean lifetime for the particular precursor mix that governs what this rate of change will be. This is another illustration of confusing the student by use of an inappropriate model (see comment for question #3). Restate the question as follows:
Question 34: (revised) Why do delayed neutrons have such a dominant effect upon reactor period?
a. short delayed neutron lifetime
b. long delayed neutron mean lifetime*
c. delayed neutrons are born at a lower energy than prompt neutrons
d. delayed neutrons have a large yield from fission
Question 37: Which of the following is true of a critical reactor brought to a prompt critical condition?
a. The reactivity addition exceeded the fast neutron fraction.
b. The prompt critical condition was achieved primarily, but not exclusively, on prompt neutrons.
c. The amount of reactivity required to achieve prompt criticality varies over core life.*
d. Flux rises at a steady, consistent rate once prompt criticality is achieved.
Comment: The asterisk indicates the intended correct answer is choice "c". Both choice b and choice d could be construed as correct. There is still a finite quantity, albeit small, of delayed neutrons present in the neutron population at prompt criticality. And, a constant reactivity value equivalent to prompt criticality will produce a stable rate, at least until thermal effects occur. The terminology of choice c ... "varies" ...is poor and not consistent with other questions. A reactor is never "brought" to prompt criticality. Restate the question as follows:
Question 37: (revised) Which of the following is true of a reactor at a prompt critical condition?
a. Reactivity exceeds the fast neutron fraction.
b. The prompt critical condition was achieved primarily, but not exclusively, on non-fission neutrons.
c. In a BWR, the reactivity required to achieve prompt criticality decreases over core life.*
d. In a BWR, flux rises at an ever accelerating period once prompt criticality is achieved.
Question 38: Explain why a "prompt jump" occurs when a step insertion of positive reactivity is made in a critical reactor.
Answer: When a step insertion of positive reactivity is made in a critical reactor, all neutrons suddenly have a higher probability of causing fission. With their very short neutron generation time, prompt neutrons respond rapidly, causing a rapid increase in neutron population (the "prompt jump"). However, as long as the reactor is kept prompt subcritical, this rapid increase in neutron population cannot be maintained. Therefore, after the initial "jump" in neutron population caused by the effect of prompt neutrons, the startup rate stabilizes at a lower value determined by the slower rate of appearance of delayed neutrons. (Reference 73, pages 7-62 through 7-66)
Comment: The answer is technically incorrect because there is no such thing as a "prompt neutron generation time" ... only a prompt neutron lifetime. The answer invokes generation time, which means that the Fission Neutron Lifecycle Model is being used to explain prompt jump ... which is impossible (see comment to question #3). Even worse, it then describes separate prompt and delayed neutron responses. In effect, two models are being mixed, The Fission Neutron Lifecycle Model and The Single Precursor Group Model. This is totally unacceptable and ridiculous. The answer also uses incorrect terminology ... startup rate instead of period. Restate the answer as follows:
Answer: (revised) When a step insertion of positive reactivity is made in a critical reactor, all neutrons suddenly have a higher probability of causing fission. With their very short lifetime, prompt neutrons respond rapidly, causing a rapid increase in neutron population (the "prompt jump"). However, as long as the reactor is kept prompt subcritical (subcritical on prompt neutrons), this rapid increase in neutron population terminates. Therefore, after the initial "jump" in neutron population caused by the effect of prompt neutrons, the reactor period stabilizes at a value determined by the slower rate of increase in the delayed neutron source strength.
Question 39: Explain why a "prompt drop" occurs when a step insertion of negative reactivity is made in a critical reactor.
Answer: When a step insertion of negative reactivity is made in a critical reactor, all neutrons suddenly have a lower probability of causing fission. With their very short generation time, prompt neutrons respond rapidly, causing a rapid decrease in neutron population (the "prompt drop"). However, delayed neutrons from precursors formed earlier (and therefore at a higher production rate due to the higher power level) will continue to appear. After the "prompt drop" in neutron population caused by the effect of prompt neutrons, the startup rate stabilizes at a less negative value controlled by the rate of appearance of delayed neutrons from the longest-lived precursors. (Reference 73, page 7-68)
Comment: This question is technically incorrect for the same reasons given for question #38. Restate the question as follows:
Answer: (revised) When a step insertion of negative reactivity is made in a critical reactor, all neutrons suddenly have a lower probability of causing fission. With their very short lifrtime, prompt neutrons respond rapidly, causing a rapid decrease in neutron population (the "prompt drop"). However, as long as the reactor is prompt subcritical (subcritical on prompt neutrons), this rapid decrease in neutron population terminates. Therefore, after the initial "drop" in neutron population caused by the prompt neutrons, the reactor period stabilizes at a value determined by the slower rate of decrease in the delayed neutron source.
Question 41: A reactor is critical with the following data:
Moderator temperature coefficient = - 5 x 10-2 % delta-K/K/°F
Decay constant (lambda) = .08 sec-1
Average effective delayed neutron fraction = .0065
How much reactivity would be needed to take this reactor "prompt critical"?
a. 5 x 10-2 % delta-K/K
b. .08 % delta-K/K
c. .65 % delta-K/K*
d. 1.7 % delta-K/K
Comment: The asterisk indicates the intended correct answer is choice "c". The question is technically incorrect because the value given for the moderator coefficient is indicated to represent (delta-K/K)/oF, whereas the coefficient represents (delta-rho)/oF. In addition, the operator never "takes" the reactor to prompt criticality. Restate the question as follows:
Question 41: (revised) A critical reactor has the following values for several important parameters:
Moderator temperature coefficient = - 5 x 10-2 % delta-rho/°F
Decay constant (lambda) = 0.08 sec-1
Average effective delayed neutron fraction = 0.0065
What reactivity value would create a "prompt critical" condition?
a. 5 x 10-2 % delta-K/K
b. .08 % delta-K/K
c. .65 % delta-K/K*
d. 1.7 % delta-K/K
Question 44: A small but rapid increase in neutron population in response to control rod motion is called a prompt
a. neutron
b. drop
c. criticality
d. jump*
Comment: The asterisk indicates the intended correct answer is choice "d". The question is technically incorrect because of poor wording ... a prompt jump does not have to be a small change in neutron population. What is small ... 30%? Restate the question as follows:
Question 44: (revised) A small but rapid increase in neutron population in response to a step change in control rod position would be classified as a prompt
a. ramp
b. drop
c. criticality
d. jump*
Question 46: A reactor is operating at a power level of 120 watts. A control rod is inserted, which results in a stable negative 80-second period. Which of the following is the best estimate of the reactor power level two minutes after rod insertion?
a. 27 watts*
b. 32 watts
c. 49 watts
d. 54 watts
Comment: The asterisk indicates the intended correct answer is choice "a". The question is technically incorrect because it does not provide sufficient information for evaluation. In particular, the power reduction during the introduction of a negative reactivity change is unknown and impossible to determine. In order to attain a -80 second period, negative reacitivity must be at least -0.0050 ... such that the associated power reduction, due to reactivity change alone, will be substantial. For a beta of 0.0064, the prompt drop in power for introduction of a -0.0050 delta-rho from criticality would be from 120 watts to 70 watts ... even before the power decay on a stable negative period begins. Restate the question as follows:
Question 46: (revised) A scram is initiated, which inserts -0.1000 delta-rho, and results in a stable negative 80-second period. Beta is 0.0064. If reactor power is 120 watts immediately after the prompt drop, what is the reactor power level two minutes after scram?
a. 27 watts*
b. 32 watts
c. 49 watts
d. 54 watts
Question 48: Reactor power increases from 5 percent to 30 percent in 12 minutes. What reactor period was required for this transient?
a. .01 seconds
b. 21.5 seconds
c. 2.5 minutes
d. 6.7 minutes*
Comment: The asterisk indicates the intended correct answer is choice "d". The question is technically incorrect because a stable period cannot be attained in the power range. Choice "d" is flawed because reactor period is given in units of seconds ... not minutes. Restate the question as follows:
Question 48: (revised) Reactor power increases from 50 kw to 300 kw in 12 minutes. What reactor period was required for this transient?
a. .01 seconds
b. 21.5 seconds
c. 150 seconds
d. 402 seconds*
Question 49: After initial criticality, the reactor period is stabilized. The source range detectors are repositioned so that the count rate is 100 cps. Sufficient positive reactivity is added to establish a 120-second period. How much time will it take for the count rate to increase to 10,000 cps with no additional operator action?
a. 1.2 minutes
b. 4 minutes
c. 9.21 minutes*
d. 15.82 minutes
Comment: The asterisk indicates the intended correct answer is choice "c". The question is technical incorrect because the answer does not account for the power increase due to the introduction of a postive reactivity change. For a stable period of 120-seconds, the reactivity would be slightly less than +0.0005. Even if this small reactivity change were input as a step, the minimum change in power level, by prompt jump, would be to 108.5 cps and the time to 10,000 counts would then be reduced to 542.8 seconds. In addition, the terminology is poor: "after initial criticality, the reactor period is stabilized" ... what does this mean? A stabilized reactor period does not have to be at steady state. Restate the question as follows:
Question 49: (revised) After establishing initial criticality, the reactor period is at infinite seconds. The source range detectors are repositioned to move count rate upscale. A positive reactivity change is introduced to establish a stable 120-second period. If the count rate on termination of control rod motion is 100 cps, how much time will it take for the count rate to increase to 10,000 cps with no additional operator action?
a. 1.2 minutes
b. 4 minutes
c. 9.21 minutes*
d. 15.82 minutes
Question 50: A reactor is at 37 percent of rated power. If a uniform reactivity addition occurs, resulting in a continuous period of +300 seconds, which one of the following is the expected reactor power level after 5 minutes?
a. 37.62 percent
b. 57.06 percent
c. 100.58 percent*
d. 370 percent
Comment: The asterisk indicates the intended correct answer is choice "c". The question is technically incorrect for two reasons. First, a stable period cannot exist in the power range and second, the power change due to the introduction of a positive reactivity change has been omitted. The wording is terrible ... what is a "uniform" reactivity insertion ... and what is a "continuous" period"? Restate the question as follows:
Question 50: (revised) After insertion of a positive reactivity increment from criticality, reactor power is at 37 kw. The stable period is +300 seconds. What will be the reactor power level after 5 minutes?
a. 37.62 kw
b. 57.06 kw
c. 100.58 kw*
d. 370 kw
Question 52: A critical reactor is at a power level of 53 watts, when a reactivity addition causes reactor power to increase on a constant period of 93 seconds. Assuming that the power increase lasts for 2.6 minutes, what will be the resulting final power?
a. 311 watts
b. 284 watts*
c. 96 watts
d. 55 watts
Comment: The asterisk indicates the intended correct answer is choice "b". The question is technically incorrect because it does not account for the power change associated with the introduction of a positive reactivity change. Restate the question as follows:
Question 52: (revised) After insertion of a positive reactivity increment from criticality reactor power is at 53 watts and the reactor period is stable at 93 seconds. Assuming that the power increase lasts for 2.6 minutes, what will be the final power?
a. 311 watts
b. 284 watts*
c. 96 watts
d. 55 watts
Question 53: During a continuous rod withdrawal accident, reactor power has increased from 387 Mw to 553 Mw in 10 seconds. What was the reactor period for this power increase?
a. 3 seconds
b. 24 seconds
c. 28 seconds*
d. 35 seconds
Comment: The asterisk indicates the intended correct answer is choice "c". The question is technically incorrect for two reasons. First a stable period cannot exist in the power range and second, a stable period cannot exist during an ongoing rod withdrawal. Restate the question as follows:
Question 53: (revised) Following termination of rod withdrawal, reactor power increases from 387 kw to 553 kw in 10 seconds. What is the reactor period for this power increase?
a. 3 seconds
b. 24 seconds
c. 28 seconds*
d. 35 seconds
Question 54: Reactor power is decreased from 225 MW to 120 MW on a reactor period of -30 seconds. How long did it take to accomplish this power decrease?
a. 2 seconds
b. 13 seconds
c. 19 seconds*
d. 47 seconds
Comment: The asterisk indicates the intended correct answer is choice "c". The question is technically incorrect because a stable period cannot exist in the power range. Restate the question as follows:
Question 54: (revised) Reactor power is decreases from 225 kw to 120 kw on a reactor period of -30 seconds. How long did it take to accomplish this power decrease?
a. 2 seconds
b. 13 seconds
c. 19 seconds*
d. 47 seconds
Question 55: Reactor power is increased over a 25-second time span on a reactor period of 135 seconds. If the final reactor power is 430 MW, what was the initial reactor power?
a. 72 MW
b. 254 MW
c. 302 MW
d. 357 MW*
Comment: The asterisk indicates the intended correct answer is choice "d". The question is technically incorrect because a stable reactor period cannot exist in the power range. Restate the question as follows:
Question 55: (revised) Reactor power is increased over a 25-second time span on a reactor period of +135 seconds. If the final reactor power is 430 kw, what was the power level at time zero?
a. 72 kw
b. 254 kw
c. 302 kw
d. 357 kw*
Question 56: Reactor power is lowered from 563 MW to 320 MW in two minutes. What is the reactor period during this load decrease?
a. -3 seconds
b. -35 seconds
c. -90 seconds
d. -212 seconds*
Comment: The asterisk indicates the intended correct answer is choice "d". The question is technically incorrect because a stable reactor period cannot exist in the power range. Restate the question as follows:
Question 56: (revised) Reactor power is lowered from 563 kw to 320 kw in two minutes. What is the reactor period during this power decrease?
a. -3 seconds
b. -35 seconds
c. -90 seconds
d. -212 seconds*
Question 61: During a reactor startup, the reactor is critical at 3000 counts per second. A control rod is notched out, resulting in a doubling time of 85 seconds. How much time is required for the reactor to reach 888,000 cps?
a. 341 seconds
b. 483 seconds
c. 698 seconds*
d. 965 seconds
Comment: The asterisk indicates the intended correct answer is choice "c". The question is technically incorrect because it does not account for power change due to the introduction of a positive reactivity change. Restate the question as follows:
Question 61: (revised) During a reactor startup, a control rod is notched out from criticality resulting in a doubling time of 85 seconds. How much time is required for the count rate to increase from 3000 counts per second to 888,000 cps?
a. 341 seconds
b. 483 seconds
c. 698 seconds*
d. 965 seconds
Question 66: Calculate the period for a reactor with a 60-second doubling time.
a. 60.0 seconds
b. 86.6 seconds*
c. 1.5 minutes
d. 6.0 minutes
Comment: The asterisk indicates the intended correct answer is choice "b". The question is in technical error because reactor period is expressed in units of seconds. Restate the question as follows:
Question 66: (revised) Calculate the period for a reactor with a 60-second doubling time.
a. 60.0 seconds
b. 86.6 seconds*
c. 90.0 seconds
d. 360 seconds
Question 67: A reactor is operating at 50 percent power with the following conditions
Power defect = 0.03% delta-K/K
Shutdown margin = 0.05% delta-K/K
Effective delayed neutron fraction = 0.007
Effective prompt neutron fraction = 0.993
How much positive reactivity must be added to take this reactor "prompt critical"?
a. 0.03% delta-K/K
b. 0.05% delta-K/K
c. 0.7% delta-K/K*
d. 0.993% delta-K/K
Comment: The asterisk indicates the intended correct answer is choice "c". The question is technically incorrect because it indicates that the values given for power defect, shutdown margin, and all four choices represent reactivity. In fact they all represent reactivity change and should be shown as delta-rho. A reactor is never "taken" to prompt critical. Restate the question as follows:
Question 67: (revised) A reactor is operating at 50 percent power with the following
Power defect = 0.03% delta-rho
Shutdown margin = 0.05% delta-rho
Effective delayed neutron fraction = 0.007
Effective prompt neutron fraction = 0.993
What positive reactivity increment would cause "prompt criticality"?
a. 0.03% delta-rho
b. 0.05% delta-rho
c. 0.7% delta-rho*
d. 0.993% delta-rho
Question 72: Two reactors are identical except that reactor A is at the end of core life and reactor B is at the beginning of core life. Both reactors are operating at 100% power when a reactor trip occurs at the same time on each reactor.
If the reactor systems for each reactor respond identically to the trip and no operator action is taken, reactor A will attain a negative ________ second stable period and reactor B will attain a negative ________ second stable period. (Assume control rod worth equals -0.9700 delta-K/K and lambda-eff equals .0124 sec-1 for both reactors.)
a. 80; 56
b. 80;80*
c. 56; 56
d. 56; 80
Comment: The asterisk indicates the intended correct answer is choice "b". The question is technically incorrect because the value of the given control rod worth is indicated to represent reactivity. In fact, it represents a change in reactivity which is delta-rho. The value of control rod worth has obviously been misstated as a value for keff after scram. No control rod in a BWR has a worth of -0.9700 delta-rho. Restate the question as follows:
Question 72: (revised) Two reactors are identical except that reactor A is at the end of core life and reactor B is at the beginning of core life. Both reactors are operating at 100% power when a reactor trip occurs at the same time on each reactor.
If the reactor systems for each reactor respond identically to the trip and no operator action is taken, reactor A will attain a negative ________ second stable period and reactor B will attain a negative ________ second stable period. (Assume control rod worth equals -0.0300 delta-rho and lambda-eff equals .0124 sec-1 for both reactors.)
a. 80; 56
b. 80; 80*
c. 56; 56
d. 56; 80
Question 74: Two reactors are identical except that reactor A is at the end of core life and reactor B is at the beginning of core life. Both reactors are operating at 100% power when a reactor trip occurs at the same time on each reactor.
If the reactor systems for each reactor respond identically to the trip and no operator action is taken, a power level of 10-5% will be reached first by reactor ____ because it has a ____________ delayed neutron fraction.
a. A; larger
b. B; larger
c. A; smaller*
d. B; smaller
Comment: The asterisk indicates the intended correct answer is choice "c". This question is included even though the answer is correct because we suspect that it is likely a correct answer for the wrong reason. We do not have access to the reference to verify this. However, similar questions for a supercritcal reactor are based on a shorter positive period at End-of-Life. In this case, trip, the prompt drop is greater at EOL and the periods for power decay in the two reactors are the same, namely - 80 seconds. Thus, reactor A does not reach the power level sooner because of a shorter negative period (see question #72).
If you disagree with any of our comments on these questions, or would care to add further enlightenment, we would appreciate hearing from you. Our E-MAIL EXPRESS is just a click away. In the next issued of NUKEFACTS we will address questions dealing with Reactivity Coefficients.