Finding Energy with the Uncertainty Principle

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SUMMARY

The discussion focuses on applying the uncertainty principle to calculate the energy required for an electron confined within a hydrogen atom. The radius of the atom is specified as 1 x 10^-10 m, which serves as Δr in the uncertainty equation Δx(Δp) ≥ ħ/4π. Participants clarify that Δr corresponds to Δx, and emphasize the importance of using the electron's mass and velocity to determine momentum for calculating kinetic energy. The final energy result should be expressed in electronvolts (eV) and rounded to the nearest hundredth.

PREREQUISITES
  • Understanding of the Heisenberg Uncertainty Principle
  • Familiarity with basic quantum mechanics concepts
  • Knowledge of electron properties, including mass and velocity
  • Ability to perform unit conversions, particularly to electronvolts (eV)
NEXT STEPS
  • Study the Heisenberg Uncertainty Principle in detail
  • Learn how to calculate kinetic energy from momentum
  • Explore the properties of electrons in quantum mechanics
  • Practice unit conversions involving energy measurements, especially to eV
USEFUL FOR

Students and educators in physics, particularly those focusing on quantum mechanics and atomic structure, will benefit from this discussion.

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Homework Statement



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.

Homework Equations



Δx(Δp)\geqh/4pie
x= position in space
p= momentum (mass)(velocity)

The Attempt at a Solution



ok I am not sure how Δr (radius) goes into the uncertainty principle, i know how it works and how it shows that it can not be exactly precise but i just don't understant how Δr would fall in the equation

is it just 1 x 10^-10 m\geq4.14x10^-15 eV/12.56637061?
 
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delta_r is your delta_x.

The speed of the electron is not relativistic. (at least I don't remember it to be)
Use the momentum to get your kinetic energy.
Then convert units.
 
o ok. and for the momentum. would i just use mass and velocity of an electron?
 

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