BELLEVUE, Wash. - In a drab one-story building here, set between an indoor tennis club and a home appliance showroom, dozens of engineers, physicists and nuclear experts are chasing a radical dream of Bill Gates.

The quest is for a new kind of nuclear reactor that would be fueled by today’s nuclear waste, supply all the electricity in the United States for the next 800 years and, possibly, cut the risk of nuclear weapons proliferation around the world.

The people developing the reactor work for a start-up, TerraPower, led by Mr. Gates and a fellow Microsoft billionaire, Nathan Myhrvold. So far, it has raised tens of millions of dollars for the project, but building a prototype reactor could cost $5 billion - a reason Mr. Gates is looking for a home for the demonstration plant in rich and energy-hungry China.

(Mr. Gates, of course, has plenty of money of his own. This year Forbes listed him as the world’s second-richest person, with a net worth of $67 billion.)

‘The hope is that we’ll find a country, with China being the most likely, that would be able to build the demo plant,