Electron Residency In Atomic Orbitals

**Strings (S _{i}P_{j}A_{jk}) = S_{7}P_{6}A_{64} Base Sequence = 12735 String Sequence = 12735 - 6 - 64 **

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Electron Residency In Atomic Orbitals

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Figure 9.16 shows the order in which the electrons of atoms fill their orbitals. Use this information to determine the electron configuration of the following elements:

(a) Iron (b) Aluminum (c) Bismuth

**The string**:

S_{7}P_{6}A_{64} (Grouping - Multi-Criteria Permutation).
**The math**:

Pj Problem of Interest is of type *grouping*. The *grouping* is ordered and the *containership* of the sub-shells are implied in the *grouping*.

The basic premise of electron residency in atomic orbitals is that the atom distributes its electrons in its orbitals so as to realized its lowest energy state. This is the reason why in period 4 (figure 9.16), the 4s sub-shell will be filled before the 3d sub-shell begins to be filled. In order words, the atoms potassium (K) and calcium (Ca) see the 4s sub-shell as a lower energy state than the 3d sub-shell.

(a) Atomic number of Iron = 26; period = 4; group = VIIIB.

So, The 3d sub-shell is filling.

So, fill all the sub-shells preceding the 3d sub-shell in period 4 (noting that s sub-shell has 1 orbital; p subshell has 3 orbitals; d subshell has 5 orbitals and f subshell has 7 orbitals. An orbital holds a maximum of 2 electrons). Then assign remaining electrons to the filling sub-shell.

So, electron configuration of iron = 1s^{2}2s^{2}2p^{6}3s^{2}3p^{6}4s^{2}3d^{6}

We then rearrange in increasing order of sub-shells

So, electron configuration of iron = 1s^{2}2s^{2}2p^{6}3s^{2}3p^{6}3d^{6}4s^{2}

(b) Atomic number of Aluminum = 13.

So, 3p sub-shell filling

So, electron configuration of aluminum = 1s^{2}2s^{2}2p^{6}3s^{2}3p^{1}

(c) Atomic number of Bismuth = 83.

So, 6p sub-shell filling

So, electron configuration of Bismuth

= 1s^{2}2s^{2}2p^{6}3s^{2}3p^{6}
4s^{2}3d^{10}4p^{6}5s^{2}4d^{10}5p^{6}6s^{2}4f^{14}5d^{10}6p^{3}

Arranging in increasing sub-shell order:

Electron configuration of Bismuth

= 1s^{2}2s^{2}2p^{6}3s^{2}3p^{6}
3d^{10}4s^{2}4p^{6}4d^{10}4f^{14}5s^{2}5p^{6}5d^{10}6s^{2}6p^{3}

The *point* **.** is a mathematical abstraction. It has negligible size and a great sense of position. Consequently, it is front and center in abstract existential reasoning.

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