German physicist werner heisenberg related the uncertainty of an object\'s position (δx) to the uncertainty in its velocity δv. the mass of an electron is 9.11× 10–31 kg. what is the uncertainty in the position of an electron moving at 2.00 × 106 m/s with an uncertainty of δv = 0.01 × 106 m/s?

Heisenberg's Uncertainty Principle gives a relationship between the standard deviation of an object's position and its momentum.

where

By definition, the momentum of the electron equals the product of its mass and velocity.

Assuming that measurement of the mass of the electron is accurate. It is assumed to be a coefficient of constant value. The standard deviation in the electron's velocity is thus directly related to that of its mass. That is:

from the question;

Convert the unit of the Planck's constant to base SI units (kg, m, s, etc.) if it was provided in derived units such as joules. Doing so would allow for a dimension analysis on the accuracy of the result.

Apply the Uncertainty Principle:

.

Dimensional analysis:

resembles the standard deviation of a position measurement. It is expected to have a unit of meter, which is the same as that of position.

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