# Step 1: Apply Heisenberg Uncertainty Principle The Heisenberg Uncertainty Principle states: \[ \Delta x \cdot \Delta p \geq \frac{h}{4\pi} \] where - \(\Delta x\) = uncertainty in position - \(\Delta p\) = uncertainty in momentum - \(h = 6.626 \times 10^{-34}\) Js (Planck constant) Given: \[ \Delta p = 1.5 \times 10^{-11} \text{ kg m/s} \] Plug in the values: \[ \Delta x \geq \frac{6.626 \times 10^{-34}}{4\pi \times 1.5 \times 10^{-11}} \] **Explanation:** We use the uncertainty principle to relate the uncertainties in position and momentum. We substitute the known values for \(h\) and \(\Delta p\). --- # Step 2: Calculate the Minimum Uncertainty in Position First, calculate the denominator: \[ 4\pi \times 1.5 \times 10^{-11} = 18.8496 \times 10^{-11} = 1.88496 \times 10^{-10} \] Now, compute \(\Delta x\): \[ \Delta x \geq \frac{6.626 \times 10^{-34}}{1.88496 \times 10^{-10}} = 3.516 \times 10^{-24} \text{ m} \] **Explanation:** By evaluating the right-hand side of the equation, we get the minimum uncertainty in the electron's position. --- # Final Answer \[ \boxed{3.52 \times 10^{-24} \text{ m}} \] *(rounded to three significant digits)* --- - **Note:** None of the answer choices given closely match this value, so please double-check if you want the answer in seconds (which would be incorrect for position uncertainty), or if there is a typo in the options. The correct units for position uncertainty are **meters (m)**, not seconds (s).