Why p- orbital, d-orbital, and f-orbitals have intensity ratios of 1:2, 2:3, and 3:4 in XPS Spectra

Why the p, d and f orbitals have intensity ratio 1:2, 2:3, and 3:4, respectively?

In XPS, the relative intensities are determined by 2j+1

nlj is the common nomenclature to represent any peaks in XPS analysis
 n : principle quantum number
 l : orbit angular momentum quantum number
 j : total angular momentum quantum number; j = l ± s (where s =±1/2 is spin angular momentum)


Subshell j values Area ratio

s 1/2 NA
p p1/2 & p3/2 1:2
d d3/2 & d5/2 2:3
f f5/2 &f 7/2 3:4


Let's prove it for p-orbital, where l=1

The intensity ratio of p1/2 & p3/2 is 1:2 corresponding to 2 electrons in the 2p3/2 level and 4 electrons in the 2p1/2 level.

Similarly for d-orbital, where l=2

The intensity ratio for d5/2 & d3/2 is 3:2

Also for f-orbital, where l=3
The intensity ratio for f7/2 & f5/2 is 4:3

To sum up, the p, d, and f- orbitals doublets peaks appear in the ration of 1:2, 2:3, and 3:4, respectively. The 1:2 for p-orbital means that the 2p1/2 contains 2- electrons while the 2p3/2 orbital contains 4- electrons. Similarly, for d, and f-orbitals, the ration can be calculated by simply using 2j+1 formula.

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