The hydrogen-like species $\mathrm{Li}^{2+}$ is in a spherically symmetric state $S_1$ with one radi

Question

The hydrogen-like species $\mathrm{Li}^{2+}$ is in a spherically symmetric state $S_1$ with one radial node. Upon absorbing light the ion undergoes transition to a state $S_2$. The state $S_2$ has one radial node and its energy is equal to the ground state energy of the hydrogen atom.

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See detailed solution for explanation.