Building the Periodic Table — Question 1

Question 1

The filling mnemonic orders equal n plus l values by principal quantum number

Use the approximate filling rule: smaller $n+l$ fills first; ties are broken by smaller n. The subshell letters s,p,d,f correspond to $l=0,1,2,3$. Consider 4s, 3d, 4p, 5s, 4d, and 5p.

1. Order the subshells according to this rule.

2. Find the total number of electron slots from 4s through 4p, inclusive.

Question 1 - Solution

The filling mnemonic orders equal n plus l values by principal quantum number

(a) Method and calculation

$$n+l:\quad4s:4;\quad3d:5;\quad4p:5;\quad5s:5;\quad4d:6;\quad5p:6.$$$$\boxed{4s\to3d\to4p\to5s\to4d\to5p}.$$

(b) Interpretation and further calculation

$$C_l=2(2l+1)\Rightarrow C_s=2,\ C_d=10,\ C_p=6.$$$$\boxed{C_{4s}+C_{3d}+C_{4p}=2+10+6=18}.$$

Physical check

This mnemonic is a useful filling guide, not a universal theorem for neutral atoms or ions. Actual orbital energies depend on occupancy and electron interactions.