The 2s and the 2p orbital energies of hydrogen atom are E_ 2s ( H ) and E_ 2p ( H ), respectively. The 2s and the 2p orbital energies of lithium atom are E_ 2s ( Li ) and E_ 2p ( Li ), respectively. The correct option(s) about the orbital energies is(are)
D. E_ 2s ( H ) > E_ 2s ( Li )
For hydrogen atom (a single-electron system), the energy of an orbital depends only on the principal quantum number n. Thus, the 2s and 2p orbitals are degenerate. E_ 2s ( H ) = E_ 2p ( H ) For lithium atom (a multi-electron system), the energy depends on both n and l. Due to the penetration effect, the 2s electron penetrates closer to the nucleus and experiences a higher effective nuclear charge than the 2p electron. Thus, the 2s orbital has lower energy than the 2p orbital. E_ 2s ( Li ) The energy of an orbital is given by E - Z_ eff ^2 n^2 . For hydrogen, Z_ eff = 1. For the 2s electron in lithium, the nuclear charge is Z=3, and it is shielded by the 1s^2 electrons. The effective nuclear charge Z_ eff for the 2s electron in Li is greater than 1 (approximately 1.3). Since Z_ eff ( Li , 2s) > Z_ eff ( H , 2s), the energy of the 2s orbital in Li is more negative than that in H. E_ 2s ( Li ) E_ 2s ( Li ) Since E_ 2p ( H ) = E_ 2s ( H ), we also have E_ 2p ( H ) > E_ 2s ( Li ). Answer: E_ 2s ( Li ) E_ 2s ( Li )
Related: Chemistry — Structure of Atom · All PYQ Banks