NUCLEAR PHYSICS QUESTION 4. [10 marks; 4 for (a), 3 each for (b) & (c)] Give res

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NUCLEAR PHYSICS QUESTION

4. [10 marks; 4 for (a), 3 each for (b) & (c)] Give results to at least 2 places after the decimal point. A reactor is coming out of a long shutdown and is reaching critical by withdrawal of Gd from the moderator. Att 0 the Gd concentration is 4 ppm, and Gd is being withdrawn at a constant rate of 0.005 ppm/min. The coefficient of reactivity of Gd is -28 mk/ppm. At t 0, an in-core detector is reading 42.00 (arbitrary units and at t 60 min, the same detector reads 46.32. (a) What was the reactivity at t 0? (b) At t 60 min, a rod of reactivity -1.5 mk is instantaneously inserted in the core. What do you predict the detector reading would be with this rod inserted? (c) The rod is instantaneously removed (the time is still t 60 min) and the Gd withdrawal continues at the same rate. At what time (measuring from t 0 will the reactor reach criticality? And what will the Gd concentration be at criticality?

Explanation / Answer

Ans a

At t=0 , the concentration of Gd is 4ppm

Reactivity of Gd = -28mK/ppm

hence the reactivity at t=0 is= (-28X4) mK= -112 mk

Ans b

Gd is being withdrawn at the rate= 0.005ppm/min

Hence in 60 min, amnount of Gd with drawn= 60X 0.005 ppm=0.3ppm

As initially 4ppm of Gd was present, the amount of Gd present after 1 hr= (4-0.3)ppm=3.7ppm

Hence the reactivity of the core=(-28X3.7) mK=-103.6 mK

Hence change in reactivity (before inserting the rod)= -103.6 mk-(-112 ) mk= 8.4 mk

And change in scale reading= 46.32-42=4.32 units

Hence change in scale reading per mk= 4.32 unit/ 8.4 mk=0.514 unit/mk

When the rod of -1.5 mk is instantaneously inserted, the change in reading will be= -0.514 X1.5 unit=-0.7715 unit

hence the reading is expected to be =(46.32-0.7715) unit=44.55 unit(approx)

Ans c

at criticallity , k=1

Hence reactivity R = (k-1)/k=0

At t=0 Gd concentration is 4ppm

Gd withdrawal rate= 0.005 ppm/min

Hence time taken to withdraw 44pm will be= 4ppm / (0.005pppm/min) =800min(starting fromt=0)

At criticallity, Gd concentration will be zero

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