Question

What major assumption (that was analogous to what had already been demonstrated for electromagnetic radiation) did de Broglie and Schrödinger make about the motion of tiny particles?

Short answer

The major assumption made by de Broglie and Schrödinger about the motion of tiny particles was that they possess both wave-like and particle-like properties, analogous to the behavior of electromagnetic radiation. This assumption, known as the de Broglie hypothesis, led to the development of wave-particle duality and the Schrödinger equation, which together form the foundation of quantum mechanics.

Step-by-step solution

Background of electromagnetic radiation

Electromagnetic radiation, such as light, exhibits both wave-like and particle-like properties. This was demonstrated by various experiments, including Young's double-slit experiment, which showed the interference patterns characteristic of wave behavior, and the photoelectric effect, explained by Einstein, which demonstrated particle-like behavior in the form of photons.

de Broglie's hypothesis

In 1924, Louis de Broglie extended the concept of wave-particle duality to all particles, specifically to tiny particles such as electrons. He hypothesized that all particles of matter, including electrons, have both wave-like and particle-like properties. This is known as the de Broglie hypothesis. According to his hypothesis, the wavelength of a particle is inversely proportional to its momentum, given by the formula: \( \lambda = \frac{h}{p} \) where \( \lambda \) is the wavelength of the particle, h is the Planck's constant, and p is the momentum of the particle.

Schrödinger's wave mechanics

In 1926, Erwin Schrödinger developed a wave equation, known as the Schrödinger equation, which describes the wave-like behavior of particles in a quantum system. The equation gives the probability distribution of particles in a system, incorporating both their wave-like and particle-like properties. Schrödinger's work built upon de Broglie's hypothesis and provided a mathematical framework for quantum mechanics. In conclusion, the major assumption made by de Broglie and Schrödinger about the motion of tiny particles was that they possess both wave-like and particle-like properties, analogous to the behavior of electromagnetic radiation. This assumption led to the development of the concept of wave-particle duality and the formulation of quantum mechanics.