Uncertainty principle and bound states?

AI Thread Summary
The discussion revolves around estimating the kinetic energy of an electron bound in a nucleus using the Uncertainty Principle, which yields approximately 200 MeV for a radius of 1 femtometer. Additionally, the binding energy of a muonic atom, which consists of a muon and a proton, is calculated to be 2.53 keV. The calculations assume a spherical nucleus and indicate that the Rydberg constant is the primary variable when substituting a muon for an electron. The participants seek clarification and assistance in understanding these concepts. Overall, the thread highlights the application of quantum mechanics principles to particle physics.
michael2k100
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i have two questions that i am struggling with and i have tried all i can think of with them and i am still not getting the answers correct.

1)Estimate, using the Uncertainty Principle, the kinetic energy of an electron if it were bound in the nucleus.

Answer: ∼ 200 MeV for R ∼ 1 fm

2)A muon is a particle very similar to an electron but with mass 105.6 MeV/c2, and a muonic atom is the bound state of a muon and a proton. Calculate the binding energy of the ground state of a muonic atom.

Answer: 2.53 keV

any possible help would be much apreciated.
 
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1. Assume that the nucleus is a perfect sphere with the given radius 1 fm.

2. The Rydberg constant is the only thing that changes when uses a muon instead of an electron.
 
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