3. An electron is revolving around a proton in a circular orbit of radius r. The proton is assumed to be stationary. The total energy of this system is 1 e? E = 2m 4T€, r where p and m denote the momentum and mass of the electron, respectively. Take the radius r to be an estimate of the uncertainty in position Ar, and the uncertainty in momentum Ap to be an estimate of p. Suppose that ArAp= ħ when the system is in the ground state. Show that the ground state energy is given by 1 те4 E, = - 2 8h2 Give the numerical value for Ej in electronvolts. Discuss if your results are consistent with Bohr's model for the hydrogen atom.

3. An electron is revolving around a proton in a circular orbit of radius r. The proton is assumed to be stationary. The total energy of this system is 1 e? E = 2m 4T€, r where p and m denote the momentum and mass of the electron, respectively. Take the radius r to be an estimate of the uncertainty in position Ar, and the uncertainty in momentum Ap to be an estimate of p. Suppose that ArAp= ħ when the system is in the ground state. Show that the ground state energy is given by 1 те4 E, = - 2 8h2 Give the numerical value for Ej in electronvolts. Discuss if your results are consistent with Bohr's model for the hydrogen atom.

College Physics

10th Edition

ISBN:9781285737027

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter27: Quantum Physics

Section: Chapter Questions

Problem 34P

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de Broglie Equation

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Question

3. An electron is revolving around a proton in a circular orbit of radius r. The proton is assumed to be
stationary. The total energy of this system is
1 e?
E =
2m
4T€, r
where p and m denote the momentum and mass of the electron, respectively. Take the radius r to be an estimate
of the uncertainty in position Ar, and the uncertainty in momentum Ap to be an estimate of p. Suppose that
ArAp= ħ when the system is in the ground state.
Show that the ground state energy is given by
1 те4
E, = -
2 8h2
Give the numerical value for Ej in electronvolts. Discuss if your results are consistent with Bohr's model for
the hydrogen atom.

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