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In a lot of the problems, the diameter of a certain atom is given to represent the uncertainty in position of an electron. How come uncertainty is measured in meters? Shouldn't the uncertainty be a volume (m^3)? Eg; not knowing where the electron is in the circular volume of an atom?
The uncertainty in position is a one-dimensional value, so you can assume that the atom is a flat shape and the uncertainty extends from left to right. A distance is a one-dimensional measurement, so the exponent is 1.
The uncertainty in position uses the same units as the units for position itself. The position of the electron is measured in meters, so the uncertainty in position is measured in meters too. I hope this helps!
Mathematically, the units of uncertainty in position must be meters in order for the other units in the Heisenberg equation to cancel out correctly while you are solving for a value. Conceptually, the reason that m is to the first power and is not m^3 is because we assume that the electron's possible position is one-dimensional, and therefore measured like a linear distance. Some questions actually state that you should model the electron as being inside of a flat square rather than a 3-D box, which can help you visualize the uncertainty in position in 1 dimension rather than within a volume. I hope this helps!
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