Final answer:
The uncertainty principle states that there is a limit to how precisely we can simultaneously know both the position and momentum of a particle. To find the minimum uncertainty in position, we can use the uncertainty principle and the uncertainty in velocity. By calculating the expression using the given values, we can determine the minimum uncertainty in position in meters.
Step-by-step explanation:
The uncertainty principle, formulated by Werner Heisenberg, states that there is a limit to how precisely we can simultaneously know both the position and momentum of a particle. The uncertainty principle is given by ΔxΔp ≥ h/4π, where Δx is the uncertainty in position, Δp is the uncertainty in momentum, and h is Planck's constant.
Given that the uncertainty in velocity is Δv = 1.88×10⁵ m/s, we can use the relation Δp = mΔv, where m is the mass of the electron, to find the uncertainty in momentum. Once we have the uncertainty in momentum, we can use the uncertainty principle to find the minimum uncertainty in position.
However, the formula above gives the product of uncertainties, so we need to take into account that we are looking for the minimum uncertainty in position rather than the product of uncertainties in position and momentum. Therefore, the minimum uncertainty in position is given by Δx ≈ h/4πΔp.
In this case, the minimum uncertainty in position can be calculated as:
Δx ≈ (6.62607015×10^(-34) J s) / (4π × 9.11×10^(-31) kg × 1.88×10⁵ m/s)
Calculating this expression will give us the minimum uncertainty in position in meters.