Multiple Choice
An electron with a mass of 9.11 x 10-31 kg has an uncertainty in its position of 630 pm. What is the uncertainty in its velocity?
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9. Quantum Mechanics
Heisenberg Uncertainty Principle
Multiple Choice
To what uncertainty (in m) can the position of a baseball traveling at 51.0 m/s be measured if the uncertainty of its speed is 0.12%? The mass of the baseball is 150 g.
A
4.2 x 10-33 m
B
5.7 x 10-33 m
C
5.9 x 10-33 m
D
4.8 x 10-33 m
Verified step by step guidance1
First, understand that this problem involves the Heisenberg Uncertainty Principle, which relates the uncertainty in position (Δx) and the uncertainty in momentum (Δp) of a particle. The principle is given by the inequality: Δx * Δp ≥ ℏ/2, where ℏ is the reduced Planck's constant (ℏ = 1.0545718 × 10^-34 Js).
Next, calculate the uncertainty in the speed (Δv) of the baseball. Since the uncertainty is given as a percentage, use the formula: Δv = (percentage uncertainty / 100) * speed. Here, Δv = (0.12 / 100) * 51.0 m/s.
Determine the uncertainty in momentum (Δp) using the formula: Δp = m * Δv, where m is the mass of the baseball. Convert the mass from grams to kilograms (150 g = 0.150 kg) before using it in the calculation.
Now, apply the Heisenberg Uncertainty Principle to find the uncertainty in position (Δx). Rearrange the inequality to solve for Δx: Δx ≥ ℏ / (2 * Δp). Substitute the values of ℏ and Δp into this equation.
Finally, calculate the value of Δx to find the uncertainty in the position of the baseball. This will give you the answer in meters, which you can compare to the provided options.
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