Final answer:
The Gold Foil Experiment, also known as Rutherford's experiment, showed the existence of atomic nuclei by directing a beam of alpha particles at a thin gold foil. The scattering of the alpha particles indicated that the gold nuclei are very small and contain most of the gold atom's mass.
Step-by-step explanation:
The classic experiment that showed the existence of atomic nuclei is known as the Gold Foil Experiment or Rutherford's experiment. In this experiment, performed by Ernest Rutherford in 1909, a beam of high-energy alpha particles was directed at a thin gold foil. The scattering of the alpha particles indicated that the gold nuclei are very small and contain nearly all of the gold atom's mass. The significant deflection of some alpha particles at large angles revealed the presence of the atomic nucleus.