He graduated from Ellston High School in 1919, and entered Drake University in Des Moines, Iowa, on an athletic scholarship.

He became interested in chemistry, and was awarded a fellowship to Iowa State College to study it there, but returned to Drake,[1] where he received his Bachelor of Arts (A.B.)

[2] After graduation, Wilhelm joined the faculty of the Intermountain Union College in Helena, Montana, where he taught chemistry and coached the football team.

[1] In February 1942, with the United States engaged in World War II, Arthur H. Compton established the Metallurgical Laboratory at the University of Chicago as part of the Manhattan Project, to build nuclear reactors to create plutonium that would be used in atomic bombs.

[4] He recruited Frank Spedding from Iowa State College as the head of the Metallurgical Laboratory's Chemistry Division.

They were able to reproduce Goggin's results in August 1942, and by September the Ames Laboratory was producing a ton of highly pure uranium metal a day.

Fears that world supplies of uranium were limited led to experiments with thorium, which could be irradiated to produce fissile uranium-233.

He was part of the United States delegation to the 1955 International Conference on the Peaceful Uses of Atomic Energy in Geneva.

He was one of 32 Drake alumni athletes who received the first Double D Awards in 1968, and he was inducted into the Iowa Boys High School Basketball Hall of Fame in 1988.