Convinced that “potentially significant” environmental problems could be avoided, federal regulators yesterday approved the largest railroad construction project in recent history. The project, a $1.4 billion, 900-mile line linking Wyoming coal fields to the Mississippi River, was okayed after the Surface Transportation Board, a branch of the Department of Transportation, imposed 147 conditions to protect water, wildlife, and air quality. The impetus for the project comes from an anticipated boom in coal mining in Wyoming’s Powder River Basin, which could produce more than 500 million tons of coal by 2010. If the project is completed, dozens of trains per day, each with at least 100 cars, would run through South Dakota’s Buffalo Gap National Grassland and Wyoming’s Thunder Basin National Grassland. Critics say they plan to sue to stop construction.