Review Test

Nuclear Reactor Theory, JU, Second Semester, 2008-2009 (Saed Dababneh).

1

Review Test

• We have done the review test.• We will discuss it later.

• Please study the review tests of last years.

http://nuclear.bau.edu.jo/Reactors/Notes/2007/ReviewTest.ppt

http://nuclear.bau.edu.jo/Reactors/Notes/2008/ReviewTest.pdf

http://nuclear.bau.edu.jo/Reactors/Notes/2007/ReviewTest.ppt

http://nuclear.bau.edu.jo/Reactors/Notes/2008/ReviewTest.pdf


2

Nuclear Fission

Asymmetry

Asymmetry

• Remember neutron excess.• (A,Z) (A,Z+1) or (A-1,Z).

Only left side of the

mass parabola.

3

Nuclear Fission

• 235U + n 93Rb + 141Cs + 2n• Q = ????• What if other fragments?• Different number of neutrons.• Take 200 MeV as a representative value.

66 MeV 98 MeV

miscalibrated

Heavyfragments

Lightfragments


165 MeV average kinetic energy carried

by fission fragments per

fission.


4

Nuclear Fission• neutrons emitted per fission.• depends on fissioning nuclide and on neutron energy inducing fission.

India?

5

Nuclear Fission• Mean neutron energy 2 MeV.• 2.4 neutrons per fission (average) 5 MeV average kinetic energy carried by prompt neutrons per fission.

• Show that the average momentum carried by a neutron is only 1.5 % that carried by a fragment. • Thus neglecting neutron momenta, show that the ratio between kinetic energies of the two fragments is the inverse of the ratio of their masses.

1

2

2

1

m

m

E

E

140

95

98

66


6

Nuclear Fission

Distribution of fission energy

Krane sums

them up as

decays.Lost … !

Enge


7

Segrè

Lost … !

Nuclear Fission

• How much is recoverable?How much is recoverable?• What about capture gammas? What about capture gammas? (produced by (produced by -1 neutrons)-1 neutrons)

• Why c < (a+b) ?Why c < (a+b) ?

Distribution of fission energy

abc

Nuclear Reactors, BAU, 1st Semester, 2007-2008 (Saed Dababneh).


8Nuclear Reactor Theory, JU, Second Semester, 2008-2009 (Saed Dababneh).

• and emissions from radioactive fission products carry part of the fission energy, even after shut down. • On approaching end of the chain, the decay energy decreases and half-life increases. Long-lived isotopes constitute the main hazard.• Can interfere with fission process in the fuel. Example?Example? (poisoning).(poisoning).• Important for research.• -decay favors high energy ~20 MeV compared to ~6 MeV for .

• Only ~ 8 MeV from -decay appears as heat. Why?Why?

Fission Products

9

Fission Products


A, Zi

A, Z-1k

A-1, Zj

A, Z+1A+1, Z

-

-

(n,)

(n,)

dNi/dt = Formation Rate - Destruction rate - Decay Rate

iiiikkjjffii NNNNN

dt

dN

f

Ni saturates and is higher with higher neutron flux, larger “fission yield” and longer half-live.


Investigate both and giving full description for the buildup and decay of fission fragment i.

10

Fission Products


iikki NN

dt

dN

iikk NN

• Shutdown

iikk NN HW 8HW 8

HW 7HW 7

Investigate the activity, decay and gamma energies of fission products as a function of time. Comment on consequences (e.g. rod cooling).


11Nuclear Reactors, BAU, 1st Semester, 2007-2008 (Saed Dababneh).

sMeVTttxtP /)(101.4)( 2.02.011 per watt of original operating power.T = time of operation.

Fission Products

Fission product activity after

reactor shutdown?


Nuclear Fission

• The fission gamma radiation Prompt with average energy of 0.9 MeV. delayed gammas.

• Investigate how prompt Investigate how prompt gammas interact with gammas interact with water, uranium and lead.water, uranium and lead.


HW 9HW 9



13

Nuclear Fission

EeE E 29.2sinh453.0)( 036.1HW 10HW 10

The experimental spectrum of prompt neutrons is fitted by the above equation. Calculate the mean and the most probable neutron energies.


• Recoverable energy release 200 MeV per 235U fission.• Fission rate = 2.7x1021 P fissions per day. P in MW.• 3.12x1016 fissions per second per MW, or 1.2x10-5 gram of 235U per second per MW (thermal).• Burnup rateBurnup rate: 1.05 P g/day. P in MW. • The fissioning of 1.05 g of 235U yields 1 MWd of energy. • Specific Burnup Specific Burnup = 1 MWd / 1.05 g 950000 MWd/t (pure (pure 235235U !!).U !!).• Fractional Burnup Fractional Burnup = ???• Thermal reactor loaded with 98 metric tons of UO2, 3% enriched, operates at 3300 MWt for 750 days.• 86.4 t U. Specific burnup 28650 MWd/t. • Not all fissions from 235U.• Fast fission of 238U.• 238U converted to plutonium more fission.

Nuclear Fission

Work it out.

Work it out.

Actually much less (all heavy material).Actually much less (all heavy material).


15

Nuclear Fission

•Two neutrinos are expected immediately from the decay of the two fission products, what is the minimum flux of neutrinos expected at 1 km from the reactor.

)(

)()(

E

EE

f

• Capture-to-fission ratio:

• Consumption rateConsumption rate: 1.05(1+) P g/day.

• Read all relevant material in Lamarsh Read all relevant material in Lamarsh Ch. 4. We will come back to this later.Ch. 4. We will come back to this later.

4.8x1012 m-2s-1


Nuclear Fission• 3.1x1010 fissions per second per W.• In thermal reactor, majority of fissions occur in thermal energy region, and are maximum.• Total fission rate in a thermal reactor of volume V

• Thermal reactor powerThermal reactor power (quick calculation) (quick calculation)

fV

10101.3 x

VP f

th


Nuclear Fission

• It is necessary to evaluate the potential hazards associated with an accidental release of fission products into the environment.

• It is required to determine a proper cooling time of the spent fuel (before it becomes ready for reprocessing) that depends on the decay times of fission products.

• It is necessary to estimate the rate at which the heat is released as a result of radioactive decay of the fission products after the shut down of a reactor.

• The poisoning is needed to be calculated (the parasitic capture of neutrons by fission products that accumulate during the reactor operation).



Review Test

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