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 p? 1 e? E 2m 4TE, 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 me4 e 8h? E1 Give the numerical value for E, in electronvolts. Discuss if your results are consistent with Bohr's model for the hydrogen atom.
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 p? 1 e? E 2m 4TE, 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 me4 e 8h? E1 Give the numerical value for E, in electronvolts. Discuss if your results are consistent with Bohr's model for the hydrogen atom.
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