An oxygen molecule has a mass of 5.3 × 10^-26 kg and an approximate diameter of 3.6 × 10^-10 m.If the molecule is moving at 400 m/s (1000 mph)with an uncertainty in velocity of 1 m/s,the uncertainty in position A)is less than or equal to 5 × 10^-26 m. B)must be equal to 5 × 10^-26 m. C)must be equal to 1 × 10^-9 m. D)is greater than or equal to 1 × 10^-9 m.

Question

Quizplus · Accepted Answer

The uncertainty principle states that the product of the uncertainty in position (Δx) and the uncertainty in velocity (Δv) is greater than or equal to h/4π, where h is the Planck's constant. 
Thus, Δx * Δv >= h/4π
Substituting the given values,
Δx * 1 >= (6.626 * 10^-34) / (4π * 5.3 * 10^-26 * 3.6 * 10^-10)
Δx >= 1.16 * 10^-9 m
Therefore, the uncertainty in position must be greater than or equal to 1 × 10^-9 m or 1 nm (nanometer), which is option D.

An Oxygen Molecule Has a Mass of 5