Why do nuclear power plants have such wide chimneys?

 Chimneys?

You mean these things?

Those aren't chimneys. They're called cooling towers. Large power plants produce enormous amounts of heat, but only use about half of it. They have to release the remaining heat to prevent melting, so they vent it into the environment.

How do they release this heat?

If there's a sufficiently large river nearby, they use that water. If not, they build these large, chimney-like towers to release the heat through EVAPORATING WATER. Yes, these chimneys release steam and vapors, not smoke or radiation. And why these large towers? The hot water raining down the bottom of the tower causes the air inside to heat up and rise, much like a hot air balloon. This "natural draft" draws in fresh air through the zigzag openings at the base, which cools the falling water through evaporation, so the remaining puddle at the bottom stays nice and cool and returns to the power plant. The tower has to be this large to accommodate the enormous volume of air needed to cool the vast amount of water heated by the power plant.

Water, in the quantities consumed by power plants, is not cheap, partly because it is highly purified. In most cases, it is cheaper to recycle it than to obtain more of it.

Why do nuclear power plants have such wide chimneys?

These are not chimneys. They are called cooling towers. Large power plants produce huge amount of heat, but use up only about half of it. They must release the remaining heat to avoid melting, so they blow it into the environment.

How do they release it?

If there is a big enough river nearby, they use the water. But if not, they build these big chimney-LIKE towers to release heat by EVAPORATING WATER. Yes, these chimneys release steam and vapor, not smoke or radiation. And why such big towers? The hot water raining down in the bottom section of the tower causes the air to heat up and start rising inside the tower, similar to why a hot air balloon rises. This “natural draft” pulls fresh air in through the zigzag openings at the bottom, which cools the falling water by evaporation, leaving the remaining pool of water at the bottom nice and cool for return to the power plant. The tower needs to be so big to allow the huge amount of air in that's required to cool the huge amount of water heated by the plant.

Water, in the amounts the power plants use it, is not cheap, also since it is highly purified. In most cases, it’s cheaper to reprocess it than to get more of it.