Quantum Mechanics and De Broglie's Wavelength Quiz

De Broglie's hypothesis states that all moving particles have an associated wave, with a wavelength given by the equation λ = h / p, where h is Planck's constant and p is the momentum of the particle. This idea is related to Planck's quantum theory of radiation through the energy equation E = hν, where E is the energy of a photon, h is Planck's constant, and ν is the frequency of radiation. It is also related to Einstein's theory of relativity through the equation E = mc^2, where E is the energy equivalence of mass m and c is the velocity of light. Furthermore, the momentum of a photon is given by p = E / c, which relates to de Broglie's wavelength equation.

The de Broglie wavelength of a particle with mass m and velocity v is given by the equation λ = h / mv. In terms of kinetic energy, the wavelength can also be expressed as λ = h / √(2mE), where E is the kinetic energy of the particle.

De Broglie postulated that a free particle with rest mass m' moving with non-relativistic speed v' has a wave associated with it, and the wavelength of this wave is given by λ = h / p, where h is Planck's constant and p is the momentum of the particle.

In 1924, de Broglie proposed the fundamental symmetry that the wavelength of radiation is related to the momentum of a photon through Planck's constant, and this relationship must hold true for material particles as well, as expressed by the equation λ = h / p.

De Broglie considered the dynamics of a particle and stated that the wave associated with a moving particle, having a momentum mv, is related to Planck's constant and must follow the equation λ = h / p, where h is Planck's constant and p is the momentum of the particle.