quantum mechanics - What would be the associated wavelength of the particle if its velocity is zero?

What will be the wavelength of a particle whose velocity is zero?

According to de Broglie's hypothesis, then the wavelength would become infinite as the momentum is zero. But, I think for a stand still particle, its particle nature should be more dominant, as at that moment it is highly localized.

Answer

To the contrary, the slower the particle moves, the more its wavelike properties show up. Compare e.g. electron in an atom, where its energy is at its lowest, with an electron flying out of a CRT. In the former case we need quantum mechanics to describe its motion (it's where QM originates), while in the latter case classical mechanics is sufficient.

So the wavelength becoming infinite for a resting electron is a completely consistent result. And it's also consistent with Heisenberg's uncertainty principle: momentum is exactly defined while position is completely undefined.