Calculate the average potential and kinetic energies for the electron in the ground state of hydrogen.
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The total energy of electron that revolves in an orbit is equal to sum of kinetic and potential energy.
The kinetic energy due to the motion is
where m is the mass of electron and v is the velocity.
The potential energy due to the position is
where r is the radius and e is the charge on electron.
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- Compute and compare the electrostatic and gravita- tional forces in the classical hydrogen atom, assuming a radius 5.3 × 10-¹¹ m.Discuss how the Hamiltonian operator for the hydrogen atom was constructed.Taking the n=3 states as a representative example, explain the relationship between the complexity of hydrogen’s standing waves in the radial direction and their complexity in the angular direction at a given value of n. What relationship would this be considered a direct relationship or inverse relationship?
- Calculate the ionization energy of doubly ionizedlithium li2+ , which has Z=3 (and is in the ground state).Prove the angular momentum of a single electron..Problem 3: Calculate the energy changes corresponding to the transitions of the hydrogen atom. Give all your answers in eV. Part (a) From n = 3 to n = 4. Part (b) From n = 2 to n = 1. Part (c) From n = 3 to n = ∞.