While Röntgen certainly did get a Nobel Prize
for his research, it was 90% pure luck
that he managed to. His work would usher in great prestige
for German Science.
Röntgen had been applying apply a voltage to an evacuated glass tube, called a Crooks Ray Tube, and noticed when he developed some nearby photo paper that a black line had appeared through the center of the paper. Knowing that only radiation could expose the photo paper, he began suspect that he had discovered a new kind of energy. He tested various substances on the tube to decipher the properties of the new rays (absorbtion rates, mostly, as the rays did not give off any visual effect). He figured that his new X-Rays, named after the mathematical unknown x, must be a form of electromagnetic radiation. When he was done with his experiments, he published one paper on the phenomenon in 1895.
By 1900, he was very, very famous. A year later with his new rays quantified with the rest of the electromagnetic spectrum by Max Planck (another German Scientist), German Science was leading the world. But it only happened because he was a careful observer.