No, the de Broglie wavelength of a rest particle cannot be infinite. The de Broglie wavelength is a concept in quantum mechanics that relates the momentum of a particle to its wavelength. It is given by the equation:
λ = h / p
where λ is the de Broglie wavelength, h is the Planck's constant, and p is the momentum of the particle.
For a rest particle, its momentum is zero since it is not moving. Therefore, if we substitute p = 0 into the equation, we get:
λ = h / 0
Dividing by zero is undefined, so this expression does not yield a meaningful result. The de Broglie wavelength is undefined for a particle at rest.
The de Broglie wavelength is significant for particles in motion, as it relates to their wave-like properties. It provides insights into phenomena such as particle diffraction and interference. However, for particles at rest, the concept of de Broglie wavelength does not apply.