(a) For an He+ ion, do the 2s and 2p orbitals have the same energy? If not, which orbital has a lower energy?

Key Concepts

Hydrogen-like Ions

Hydrogen-like ions, such as He+, have only one electron and exhibit similar energy level structures to hydrogen. In these ions, the energy levels depend primarily on the principal quantum number (n) and the effective nuclear charge (Z). For He+, the electron experiences a stronger attraction to the nucleus compared to hydrogen, leading to different energy considerations for orbitals.

Orbital Energy Levels

In multi-electron atoms, orbitals of the same principal quantum number (n) can have different energy levels due to electron-electron interactions and shielding effects. However, in hydrogen-like ions, the 2s and 2p orbitals are influenced by the same effective nuclear charge, but the 2s orbital is lower in energy than the 2p orbital due to its spherical shape and closer proximity to the nucleus.

Penetration and Shielding

Penetration refers to how close an electron can get to the nucleus, while shielding describes how inner electrons can reduce the effective nuclear charge felt by outer electrons. The 2s orbital penetrates closer to the nucleus than the 2p orbital, resulting in lower energy for the 2s orbital in He+. This difference in penetration leads to the 2s orbital being more stable and lower in energy compared to the 2p orbital.