Final answer:
According to the uncertainty principle in quantum mechanics, the electron will have a smaller uncertainty in position compared to a proton when their uncertainties in momentum are the same.
Step-by-step explanation:
The uncertainty principle in quantum mechanics states that it is impossible to simultaneously measure the position and momentum of a particle with perfect accuracy. The uncertainty in position, denoted as Δx, and the uncertainty in momentum, denoted as Δp, are related by the inequality ΔxΔp ≥ h/4π, where h is Planck's constant. Therefore, when the uncertainty in momentum is the same for an electron and a proton, the uncertainty in position will be smaller for the electron. This is because the mass of an electron is smaller than the mass of a proton, and hence the uncertainty in momentum, given by Δp = mΔv, will be smaller for the electron.