Question

According to wave mechanics, a material particle is associated with
A) a single wave
B) a wave packet
C) two progressive waves
D) a ripple

Answer 1

Light was found to exhibit wave-like behavior as well as particle-like behavior. This discovery implied that matter can also be treated as a wave where each particle will be considered as a quantum of energy or packet of energy.

Complete step by step answer:
One of the most important results of Einstein’s photoelectric effect is that light is made up of packets or quanta of energy called photons. Up until then, radiation was considered to behave like a wave-based on phenomena like diffraction, interference, and polarization. But the photoelectric effect gave strong evidence to support the theory that radiation posses dual nature.
So this led to de Broglie’s argument that the opposite must also be true i.e., the matter must correspondingly exhibit wave nature where a particle of the matter can be associated with a wave packet in a wave. de Broglie's arguments were based on the fact that nature is symmetrical and that matter and energy which are considered as the two basic entities must therefore be symmetrical too.

Thus a particle is associated with a wave packet in wave mechanics. So, the correct option is B.

Note:
The photoelectric effect deals with the interaction of light with matter (a metal surface) and on striking the metal surface, light behaves as if it was made up of packets or quanta of energy. However, It is important to remember that the nature of the experiment will determine whether the particle nature or wave nature is preferred to understand the experiment.