## Indeterminacy in Position [ENDORSED]

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

Kelvin Chung 1C
Posts: 50
Joined: Sat Aug 24, 2019 12:15 am

### Indeterminacy in Position

In the 10/14/19 lecture, Dr. Lavelle gave an example problem:

Incorrect atomic model: electron is located inside the nucleus of the atom. For the H-atom, the electron is then confined to its nuclear diameter.

He explained that the nuclear diameter would be the value for the electron's indeterminacy in position, or Δx. Can someone explain why this is?

Jainam Shah 4I
Posts: 130
Joined: Fri Aug 30, 2019 12:16 am

### Re: Indeterminacy in Position  [ENDORSED]

Dr. Lavelle was using the indeterminacy principle to show how the old model of the atomic structure was incorrect. Prior to the recent atomic model, many believed that the electron was housed within the nucleus of the atom. The electron could be anywhere within the diameter of the nucleus. Thus, the diameter can be used to represent delta x or the possible position of the electron. However when we used the diameter of the nucleus as the position of the electron we found that that the speed of the electron was higher than the speed of light. We then see why electrons cannot be contained within the nucleus and rather lie in orbitals around the nucleus with each orbital corresponding to a specific energy level.

Leila_4G
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Joined: Sat Sep 14, 2019 12:17 am

### Re: Indeterminacy in Position

So what distance does Δx represent on the electron level? The change in position between the first energy state and the second?

Alexa Mugol 3I
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Joined: Sat Aug 17, 2019 12:17 am

### Re: Indeterminacy in Position

To answer Leila's question, Δx represents the indeterminacy in position of the e-, or the possible places to find the e-. Since we suppose that the e- is possibly in the nucleus, we would use the diameter of the nucleus to represent the uncertainty in position. It would not have anything to do with energy levels because in this incorrect atomic model, we assume that the e- is in the nucleus (so it wouldn't be in energy levels in this model).

Chantel_2I
Posts: 109
Joined: Sat Sep 07, 2019 12:19 am

### Re: Indeterminacy in Position

Leila_4E wrote:So what distance does Δx represent on the electron level? The change in position between the first energy state and the second?

Delta X is the distance in which the electron can be found. For example, in the particle in a box problem, delta x would be the diameter of the box. In atoms, we usually use the diameter of the atom as delta x.

Sydney Myers 4I
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Joined: Fri Aug 09, 2019 12:17 am

### Re: Indeterminacy in Position

Alexa Mugol 3I wrote:To answer Leila's question, Δx represents the indeterminacy in position of the e-, or the possible places to find the e-. Since we suppose that the e- is possibly in the nucleus, we would use the diameter of the nucleus to represent the uncertainty in position. It would not have anything to do with energy levels because in this incorrect atomic model, we assume that the e- is in the nucleus (so it wouldn't be in energy levels in this model).

I understand why we use the size of the nucleus in this problem, but my question is why wouldn't we use the volume instead? Or area? Why is the diameter the chosen measurement?