Uncertainty Principle and energy of an electron

Click For Summary

Discussion Overview

The discussion revolves around applying the uncertainty principle to calculate the energy required for an electron to be confined within a hydrogen atom. Participants explore the relationship between position uncertainty and momentum, as well as the implications for kinetic and potential energy within the context of atomic structure.

Discussion Character

  • Homework-related
  • Mathematical reasoning
  • Conceptual clarification

Main Points Raised

  • One participant attempts to use the uncertainty principle, stating Δx(Δp) ≥ h/4π and calculates Δp based on a given radius for the hydrogen atom.
  • Another participant suggests that the expression p²/2m could represent kinetic energy, while e²/Δx might estimate potential energy.
  • A third participant provides an analogy involving escaping Earth's atmosphere to clarify the relationship between kinetic and potential energy, emphasizing the need for sufficient energy for the electron to remain in the atom.
  • A later reply calculates kinetic energy using the previously derived Δp and questions the potential energy required for the electron's confinement.

Areas of Agreement / Disagreement

Participants express varying levels of understanding and confidence in their calculations and interpretations of the uncertainty principle. There is no consensus on the correct approach or final values, and the discussion remains unresolved.

Contextual Notes

Participants express confusion regarding the application of the uncertainty principle and the calculations involved. There are indications of missing assumptions and unresolved mathematical steps, particularly in relating kinetic and potential energy.

Xclusive
Messages
2
Reaction score
0
Using the uncertainty principle find the energy required for the electron to be confined inside the hydrogen atom. Use the radius of the atom 1 x 10-10 m for Δr. Express your answer in eV, rounded up to the nearest hundredth.

Equations used

Δx(Δp) ≥ h/4pie

1 x 10^-10 m x p ≥ 4.14 x 10^-15 eV / 12.56

Δp ≥ 3.3 x 10^-6

I'm not really sure what to do from here or if I even did this correctly. My teacher did a horrible job explaining this to me and I am really confused. I found the momentum Δp = mv

What do I do from here?
 
Physics news on Phys.org
Maybe p2/2m is an estimation of kinetic energy. Maybe e2/delta_x is an estimation of the potential energy?
 
This problem is rather confusing and basically it's way of approximating values using the uncertainty principle so I wouldn't worry too much the first time you encounter it!

Think in terms of energy.

For example say you want to know how much energy it takes to leave the Earth's atmosphere. Well the Earth has some potential energy right? We can consider this like a potential energy well, the Earth is a well and in order to escape we must put in energy to overcome the potential. So if start from the ground and wanted to leave the Earth's atmosphere we would need a greater amount of kinetic energy than potential energy. Or conversely in order to stay in the Earth's atmosphere the potential energy of the Earth would need to be greater than our kinetic energy.

So back to your problem. In order for the electron to stay in the hydrogen atom there must be a greater or equal amount of potential energy compared to kinetic energy does this make sense?
 
Ok so

Δp ≥ 3.3 x 10^-6 eVs

p^2/2m = Ke
(3.3x10^-6)^2 eVs / 2 (1.01)

Ke = 5.5 x 10^-12 eVs

So U ≥ 5.5 x 10^-12 eVs?
 

Similar threads

Graduate Is this a valid derivation of the Uncertainty Principle?
  • · Replies 3 ·
Replies
3
Views
2K
Graduate Can scattering experiment be used to determine location and momentum of an electron?
  • · Replies 2 ·
Replies
2
Views
1K
Undergrad Heisenberg uncertainty principle and the canonical momentum operator
  • · Replies 32 ·
2
Replies
32
Views
4K
Graduate Angular momentum uncertainty principle and the particle on a ring
  • · Replies 5 ·
Replies
5
Views
3K
High School An application of the uncertainty principle
  • · Replies 2 ·
Replies
2
Views
3K
Undergrad Measurement problem - will this work?
  • · Replies 4 ·
Replies
4
Views
3K
Undergrad Uncertainty of electron energy based on confinement radius?
  • · Replies 2 ·
Replies
2
Views
2K
High School Does Wavelength Affect Uncertainty in Macroscopic Objects?
  • · Replies 11 ·
Replies
11
Views
3K
Graduate Understanding Electron Movement with Heisenberg's Uncertainty Principle
  • · Replies 6 ·
Replies
6
Views
2K
Graduate Is this statement about the Uncertainty Principle correct?
  • · Replies 4 ·
Replies
4
Views
2K