## Units for Uncertainty in Position

$\Delta p \Delta x\geq \frac{h}{4\pi }$

Posts: 126
Joined: Wed Sep 30, 2020 9:58 pm

### Units for Uncertainty in Position

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?

Yasmina Zaarour 1G
Posts: 93
Joined: Wed Sep 30, 2020 9:51 pm
Been upvoted: 1 time

### Re: Units for Uncertainty in Position

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.

Samantha Pedersen 2K
Posts: 127
Joined: Wed Sep 18, 2019 12:21 am
Been upvoted: 9 times

### Re: Units for Uncertainty in Position

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!

Frankie Mele 3J
Posts: 99
Joined: Wed Sep 30, 2020 10:09 pm

### Re: Units for Uncertainty in Position

The units also have to be in meters because when using uncertainty of position to solve for delta velocity, your final answer has to be in (m/s).

Mackenzie Van Val 3E
Posts: 103
Joined: Wed Sep 30, 2020 9:36 pm
Been upvoted: 1 time

### Re: Units for Uncertainty in Position

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!

Aayushi Jani 3A
Posts: 104
Joined: Wed Sep 30, 2020 9:51 pm

### Re: Units for Uncertainty in Position

The uncertainty in position refers to the position of the electron (which is in meters), so it would also be in meters.

Stacey Phan 2I
Posts: 104
Joined: Wed Sep 30, 2020 9:59 pm
Been upvoted: 1 time

### Re: Units for Uncertainty in Position

Use meters so the units cancel out correctly!