Electronic configurations

Question P2.5.12

The electron configuration of an atom is the specification of the distribution of its electrons in atomic orbitals. An atomic orbital is identified by a principal quantum number, $n = 1,2,3,\cdots$ defining a shell comprised of one or more subshells defined by the azimuthal quantum number, $l=0,1,2,\cdots{n-1}$. The values $l=0,1,2,3$ are refered to be the letters $s$, $p$, $d$, and $f$ respectively. Thus, the first few orbitals are: 1s ($n=1, l=0$), 2s ($n=2, l=0$), 2p ($n=2, l=1$), 3s ($n=3, l=0$), and each shell has $n$ subshells. A maximum of $2(2l+1)$ electrons may occupy a given subshell.

According to the Madelung rule, the $N$ electrons of an atom fill the orbitals in order of increasing $n+l$ such that whenever two orbitals have the same value of $n+l$, they are filled in order of increasing $n$. For example, the ground state of Titanium ($N=22$) is predicted (and found) to be $1s^22s^22p^63s^23p^64s^23d^2$.

Write a program to predict the electronic configurations of the elements up to Rutherfordium ($N=104$). The output for Titanium should be

Ti: 1s2.2s2.2p6.3s2.3p6.4s2.3d2

A Python list containing the element symbols is here: element_symbols.py

As a bonus exercise, modify your program to output the configurations using the convention that the part of the configuration corresponding to the outermost closed shell, a noble gas configuration, is replaced by the noble gas symbol in square brackets, thus:

Ti: [Ar].4s2.3d2

the configuration of Argon being 1s2.2s2.2p6.3s2.3p6.


Solution

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