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At the end of electronic configuration, we were taught that, electron orbitals are most stable when they are either fully filled or half filled. E.g., the final valence configuration of chromium is $\ce{(4s)^1 (3d)^5}$ and not $\ce{(4s)^2 (3d)^4}$. But the final electronic configuration of chlorine is $\ce{(3s)^2 (3p)^5}$ and not $\ce{(3s)^1 (3p)^6}$.

Why doesn't chlorine follow the half filled or full filled theory?

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Having a half-filled or filled subshell is stabilising, as you say. But for Cl, the difference in energy between 3s and 3p is greater than the additional stabilisation from filling the 3p subshell. 3d and 4s are closer in energy, so for Cr it is favourable to promote a 4s electron and have a 4s1 configuration.

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In the case of 3$d$ and 4$s$ energies, there is an "anomaly" in the ordering, being the 3$d$ orbital energy higher than that of 4$s$. However, you are comparing the configuration of chromium (with 3$d$ and 4$s$ orbitals) with chlorine. The valence shell of the latter contains 3$s$ and 3$p$ orbitals, and the energy of 3$s$ orbitals are lower than that of 3$p$.

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