A nuclear reactor is a device in which a sustained chain reaction takes place - Leaving Cert Physics - Question 8 - 2014

A common example of a moderator used in nuclear reactors is water, specifically heavy water (D2O).

(i) A moderator is needed to slow down the fast neutrons produced during fission. Slower neutrons have a higher probability of being absorbed by the fuel nuclei, which is crucial for sustaining the chain reaction.

(ii) Control rods absorb neutrons and can be inserted or removed from the reactor core to increase or decrease the number of available neutrons, thus controlling the rate of the reaction.

A heat exchanger transfers thermal energy from one fluid to another without mixing them. In a nuclear reactor, hot coolant from the reactor passes through the heat exchanger, where it transfers heat to water, turning it into steam to drive a turbine. It's necessary to use a heat exchanger to convert the thermal energy produced in the reactor into mechanical energy efficiently while maintaining the separation between radioactive coolant and the steam used for electricity generation.

The nuclear reaction can be expressed as:

$^{238}_{92} ext{U} + n \rightarrow ^{239}_{93} ext{Pu} + 2 \beta^-$

To find the number of uranium-235 nuclei required:

1. Calculate the energy per day:

   • Power = Energy/Time => Energy = Power × Time
   • $1 ext{ GW} = 1 imes 10^9 ext{ W}$, for 1 day (86,400 seconds):
   • Energy = $1 imes 10^9 imes 86,400 = 8.64 imes 10^{13} ext{ J}$

2. Calculate the total energy produced by one fission:

   • Each fission produces 202 MeV = $202 imes 1.6 imes 10^{-13} ext{ J} = 3.232 imes 10^{-11} ext{ J}$

3. Calculate the number of fissions required:

   • Number of fissions = Total Energy / Energy per fission = $\frac{8.64 \times 10^{13}}{3.232 \times 10^{-11}} \approx 2.67 \times 10^{24}$

Thus, approximately $2.67 \times 10^{24}$ uranium-235 nuclei are required.