Hydrogen Atom

This text discusses the degeneracy of hydrogen-like energy levels and the ground state of a hydrogen-like atom.

Degeneracy

Degeneracy is the number of states with the same energy.

In the nth hydrogen-like energy level, there are n^2 degenerate states.

Ground State

The ground state of a hydrogen-like atom is the state with the lowest energy.

The wave function of the ground state of a hydrogen-like atom is given by the expression:

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R_n^s(r) Y_00(theta, phi) = (2/na^3)^(1/2) exp(-r/na)
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The energy of the ground state of a hydrogen-like atom is given by the expression:

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E_n^g = -13.6 eV / n^2
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