If a particle's position is precisely known, what is the most direct consequence on its momentum according to quantum mechanics?

If a particle’s position is known exactly, the uncertainty in its position Δx is essentially zero. According to the Heisenberg uncertainty principle, Δx Δp ≥ ħ/2, so when Δx approaches zero the product forces Δp to become very large. This means the particle’s momentum is completely uncertain, spanning an infinite range of possible values. For example, if you pinpoint a particle’s location to a single point on a screen, its momentum could be anything from negative to positive infinity, making it impossible to predict its motion. Thus, knowing a particle’s position precisely destroys any useful knowledge of its momentum.