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Nuclear Fission

Q2.

(a) When a nucleus of uranium-235 fissions into barium-141 and krypton-92, the change in mass is 3.1 × 10–28 kg.

Calculate how many nuclei must undergo fission in order to release 1.0 J of energy by this reaction.

For one fission reaction:

ΔE = Δmc2

ΔE = 3.1 × 10–28 × (3.00 x 108)2

ΔE = 2.79 × 10–11J

Number of nuclei required to release 1.0 J

= 1.0 / 2.79 × 10–11J

= 3.5(8) × 1010

(2 marks)

(b) A nuclear power station produces an electrical output power of 600 MW. If the overall efficiency of the station is 35%, calculate the decrease in the mass of the fuel rods, because of the release of energy, during one week of continuous operation.

If the output of a 35% efficient station is 600 MW then the nuclear fuel must have produced a lot more energy than that at the fission stage. You first of all need to work out how much energy the fuel would have produced.

Let the power output of the nuclear fuel be N

600 MW = 35% and N = 100%

so 600/N = 35/100 = 0.35

therefore N = 600/0.35 = 1.71 x 103 MW

N = 1.71 x 109 W

This means that 1.71 x 109 J of energy was produced by mass being converted to energy in the fission process every second. In 1 week there are 7 x 24 x 602 seconds so:

Energy produced by fission each week = 7 x 24 x 602 x 1.71 x 109 J = 1.03 x 1015 J

E = Δmc2

Δm = E/c2

Δm = 7 x 24 x 602 x 1.71 x 109/(3.0 x 108)2

Δm = 1.1(5) x 10-2kg

(1.14 x 10-2kg if you used the 1.03 x 1015 J)

Δm = 0.0115kg = 11.5g of fuel – amazingly tiny, eh?

(4 marks)

(Total 6 marks)