How does a nuclear power plant produce electricity?

this need to be credible it is for a chemistry class

Answer:
It is by the process of nuclear fission - heavy radioactive nuclei such as uranium absorbs a neutron, making them unstable, causing them to split to from two lighter nuclei and release energy. This energy is due to the loss in mass (mass defect) between the uranium and the product nuclei when it splits, this mass being converted to heat energy via E = mc^2.

This heat is transferred to water in pipes flowing through the reactor core to a heat exchanger, which causes the water to boil and form steam. This steam passes through a series of turbines which are attached to a coil of wire. This coil spins rapidly cutting a magnetic field to generate electrcity via electromagnetic induction.

The nuclear reaction is self propagating - a chain reaction. Each split of the uranium releases 3 more neutrons which are absorbed by other nuclei which again split and so on. This reaction is prevented from going out of control (core meltdown) by control rods, which traps some of the neutrons produced, preventing them from being absorbed.
fusion
it has nothing really to do with chemistry.

I worked on and operated a nuclear power plant for 6 years... so I know what Im talking about.

Materials undergo physical change and nuclear change... but no chemical (molecular) change.

A nuclear reaction is different from a chemical reaction.

Nuclear fussion causes radiation in many forms... one of which is the production of heat. Heat gets transferred to water... waters heat causes boiling. boiling causes steam pressure... steam pressure turns a turbine. That turbine is connected by a common axle to an electric generator, in which magnetism and conductive wires produce electricity.

It is way way more complex than that... and most of it is classified on some level. But those are the essentials.

See, no chemistry involved. Nuclear work, thermal work, mechanical work... nuclear change, physical change. Not really any chemical change.

The only chemical changes that occur are the waste byproducts of the nuclear reaction and of course the chemicals we add to the water to prevent corrosion.
It uses a controlled nuclear reaction to produce energy which spins turbines. These turbines move through a magnetic field. Cutting through a magnetic field creates electric current.

That's the simple explanation, at least.

(note: I could be totally wrong. But that's my understanding of it.)
They use nuclear fuel rods to heat water. This produces steam which is used to drive steam turbines which turn magnetos making---taadaa! electricity.
The nuclear reaction is used to generate steam. The steam turns turbines which turn generators which make electricity.
A critical mass of fissionable matter (uranium) is assembles and controlled by moderation (moderation is a mass of lightweight element, it can be graphite, light water or heavy water; that reduce the speed of emitted neutrons so they have a greater probability of fissioning another nucleus.
Each fission release a few neutrons, and two nucleus that are lighter than the original one, and a lot of energy in the form of heat.
A heat transport fluid -- usually water -- is thus heated by the on going nuclear fission. This hot water is used to heat a secondary water circuit (the primary tend to be slightly radio-active, so it does not leave the reactor building). The secondary water circuit is allowed to boil, and that steam drives turbines that are connected to electrical generators.
Credible? How's this... I hold a Q level security clearance from the US NRC. I worked in nuclear plants for 2 years.
The main part of the sequence to generate power form nuclear energy is the reactor core. In the core, a self-sustaining nuclear fission reaction is taking place. The splitting of the Uranium 235 nucleus by a neutron causes the ejection of 2 neutrons which in turn, splits two more nucleus'. Along with the neutron ejection is the releases of an enormous amount of energy in the form of heat. A coolant, typically water is circulated under high pressure to this core. The pressure allows the water to gain heat energy but remain a liquid. After the coolant leaves the reactor containment area, the pressure is suddenly reduced. This forms steam, which is used to turn giant turbines connected to equally impressive generators. These create the electrical power. The expended lower pressure steam is condensed and then returns to the core to do the cycle again.
An advanced gas-cooled reactor(AGR) generally has enriched uranium as it's fuel.A Water-Cooled Reactor, such as the steam generating heavy water(deuterium oxide ) reactor,has water circulating through the hot core.The water is converted to steam, which drives turbo-alternators for generating electricity.
Spontaneously emitted neutrons from certain heavy, radioactive elements such as uranium are slowed by a substance such as regular water or heavy water (moderator) so that they can interact with other nuclei. When those nuclei split, they release energy and more neutrons. The nuclear fuel is geometrically arranged to limit the rate of splitting (fission). Additionally, control rods, which absorb neutrons, are kept at least somewhat inserted to limit the rate. A very large amount of heat, and radiation which turns into heat, is released. This heat is converted to steam which drives turbines. At the point where turbines are driven, a nuclear plant doesn't differ at all from a hydro plant or a coal-fired plant. Fusion technology has not reached a commercial stage yet. Fission is the only way substantial amounts of energy are generated by nuclear reaction.

Larry, with respect, I don't know what level Q is in the NRC, but it sounds impressive. That said, isn't it a liability to advertise your access to nuclear techonology, especially in the post-9/11 world? Like the CIA says, you only hear about their failures.
The nuclear reaction of fission takes place, splitting uranium atoms and producing a great deal of heat. The heat is used to boil water and make steam to turn turbines and generate electricity in the same manner as a coal fired plant. Radiation is contained in the containment building, extra heat is disapated in the cooling towers. Spent fuel rods are eventually buried.
I just wanted to let you know that it IS Chemistry more than anything. Larry L. has the best description that I looked through. The last respondant seemed to know the jist, but it is all chemical. If you want to learn about the most efficient type of nuclear power you should look to the French. They use one of the biproducts (Plutonium) to make more energy.
That is all.

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