Chapter 3.8, Problem 3.8.3SR

Interpretation Introduction

Interpretation:

The orbitals which are lower in energy than 3p orbital in hydrogen atom should be explained.

Concept Introduction:

The energies of orbitals in the hydrogen atom depend on the value of the principal quantum number ($n$).  When $n$ increases, energy also increases.  For this reason, orbitals in the same shell have the same energy in spite of their subshell.

The increasing order of energy of hydrogen orbitals is

$1s<2s=2p<3s=3p=3d<4s=4p=4d=4f$

One 2s and three 2p orbitals have the same energy in the second shell. One 3s, three 3p and five 3d have the same energy in the third shell.  All sixteen orbitals which are one 4s, three 4p, five 4d and seven 4f in the fourth shell have the same energy.

Figure 1

The energy levels of the different orbitals in hydrogen atom are easily explained by considering the given diagram.  Here, each box represents one orbital. Orbitals with the same principal quantum number ($n$) have the same energy.