Final answer:
The uncertainty in the position of an electron can be calculated using Heisenberg's Uncertainty Principle, given the mass of the electron and the uncertainty of its velocity. By calculating the uncertainty in momentum and applying the principle, the uncertainty in position is found.
Step-by-step explanation:
The student is asking about the uncertainty in the position of an electron given the uncertainty in its velocity using Heisenberg's Uncertainty Principle. To calculate this, we use the principle that states Δx Δp ≥ ℏ/2, where Δx is the uncertainty in position, Δp is the uncertainty in momentum, and ℏ is the reduced Planck's constant (ℏ = h / (2π), h = Planck's constant = 6.626 × 10^-34 m^2 kg/ s).
The momentum of the electron (p) is the product of its mass (m) and velocity (v), so Δp can be found by multiplying the mass of the electron by the uncertainty of its velocity, Δv. Given that the mass of an electron is approximately 9.11 × 10^-31 kg, and the uncertainty in its velocity is 1.63 × 10^5 m/s, the uncertainty in its momentum (Δp) is (9.11 × 10^-31 kg) × (1.63 × 10^5 m/s).
Once Δp is calculated, we can rearrange the Heisenberg principle to solve for Δx: Δx ≥ ℏ / (2 Δp). After inserting the known values, we can calculate the uncertainty in the position of the electron. This gives us a quantitative measure of the uncertainty in our knowledge of where the electron is, which is a crucial concept in quantum mechanics.