Final answer:
Max Planck proposed the quantization of energy levels to resolve the ultraviolet catastrophe associated with the blackbody spectrum, a problem where classical physics predicted incorrect and infinite ultraviolet emissions.
Step-by-step explanation:
The aspect of the blackbody spectrum that led Max Planck to propose the quantization of energy levels in atoms and molecules is known as the ultraviolet catastrophe. The classic Rayleigh-Jeans law, which was based on classical physics, predicted an infinite increase in the emission of ultraviolet light as wavelengths got shorter, which did not match experimental observations. Planck resolved this issue by introducing the innovative concept that energy could only be exchanged in discrete amounts, or quanta. The quantized oscillators in Planck's model successfully described the experimentally observed shape of the blackbody spectrum, demonstrating that energy states could not take on any continuous value, which was a significant departure from the principles of classical physics.