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Arranging atomic orbitals in increasing energy order. Explain this in detail.

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Last updated date: 23rd Jul 2024
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Answer
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Hint: Atomic orbital is a mathematical function that provides insight into the wave nature of electrons that exist around the nuclei of atoms. These mathematical functions are often employed in order to determine the probability of finding an electron in a specific region around the nucleus of the atom.

Complete answer:
Orbitals are arranged with increasing energy on the basis of $ (n + l) $ rule. If the value of $ (n + l) $ for an orbital is higher, then it has higher energy. Similarly, the lower value of $ (n + l) $ for an orbital signifies lower energy.
Based on above discussion, the arrangement of atomic orbitals in increasing order of energy can be done as follows:
First write the shells one below the other in a column. This should be in increasing order of $ n $ value and the subshells should be in the same row.
Then draw a slanting arrow, from top to bottom. The ending of the arrow must be with a new orbital.
The above two steps need to be repeated whenever the $ s - $ subshell is reached.
At last, write the subshells in the order of moving arrows.
Hence, the subshells in increasing energy order can we written as:
 $ 1s{\text{ }}2s{\text{ }}2p{\text{ }}3s{\text{ }}3p{\text{ }}4s{\text{ }}3d{\text{ }}4p{\text{ }}5s{\text{ }}4d{\text{ }}5p{\text{ }}6s{\text{ }}4f{\text{ }}5d{\text{ }}6p\;7s\;5f\;6d\;7p\;8s\;5g\;6f\;7d\;8p $ .

Note:
While writing the electronic configuration of any element, one should remember that the electrons of an element are filled according to the order of increasing energies of orbitals. For example, in iron the electronic configuration is $ [Ar]4{s_2}3{d_6} $ . The electron first occupies the lower $ 4s $ orbitals and then enters into higher energy $ 3d $ orbital.