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Question

In He+, the electron is initially present in an orbital that has no radial nodes but in which the sign of the wave function changes once across a plane. On absorbing a photon with an energy which is 75% of the ground state energy of hydrogen, the electron moves to a higher orbital. Find the sum of principal quantum numbers of the initial and final orbitals of the electron.

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Solution

Initially, electron is in orbital with no radial nodes,
So nl1=0; and wavefunction changes sign once across a plane i.e., there is one angular node so l=1
n=2
Hence initially electrons is in 2p.
Now this electron absorbs 75100×13.6 eV or 34×13.6 eV energy to move to higher orbit (shell)
In He+,
E1=4×13.6 eV
E2=4×13.64 eV=13.6 eV
E3=4×13.69 eV
E4=4×13.616 eV=13.64 eV
Hence we can see that E4E2=34×13.6 eV
Hence electron goes to the 4th shell.
So, ninitial+nfinal=2+4=6

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