Finding Energy with the Uncertainty Principle

AI Thread Summary
The discussion revolves around applying the uncertainty principle to calculate the energy required for an electron confined within a hydrogen atom, using a radius of 1 x 10^-10 m for Δr. Participants clarify that Δr corresponds to Δx in the uncertainty equation, which relates position and momentum. The momentum of the electron is calculated using its mass and velocity, with the kinetic energy derived from this momentum. There is a focus on ensuring the speed of the electron is non-relativistic for accurate calculations. The conversation emphasizes the importance of unit conversion and proper application of the uncertainty principle in this context.
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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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