Final answer:
If the uncertainty in momentum of an electron is zero, then the uncertainty in its position would be infinite.
Step-by-step explanation:
The Heisenberg's uncertainty principle states that the product of the uncertainties in position (Δx) and momentum (Δp) of a particle is on the order of Planck's constant (h).
Hence, if there is no uncertainty in momentum (Δp = 0), the uncertainty in position (Δx) must be infinitely large.
This is because the electron displays wave-particle duality, where it has characteristics of both waves and particles.
With a completely certain momentum, implying a specific wavelength and wave number, the electron could be found anywhere along the x-axis, hence an infinite uncertainty in position.
Mathematically, if we take the uncertainty in position Δx to be tending to zero to know the electron's position precisely, the momentum's uncertainty Δp must tend towards infinity to satisfy the uncertainty principle, which is ΔxΔp ≥ h/4π, or the reduced form ΔxΔp ~ ħ/2, where ħ is the reduced Planck's constant.