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I am a bit confused on the definition of a chiral center;

A carbon atom is chiral if it has four different items bonded to it at the same time. source

However I am not sure whether different alkyl groups such as $\ce{CH_3}$ or $\ce{C_5H_{11}}$ on a single carbon count as "different" items, or do only different functional groups count?

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    $\begingroup$ See, you did not say "identical alkyl groups such as CH3 or C5H11". Why? Because you know they are different. Yes, that counts. $\endgroup$ – Ivan Neretin Aug 19 '20 at 15:56
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    $\begingroup$ Also, keep in mind that it is not limited to carbon with 4 different groups. For example, if you look at other elements with different ligands in inorganic compounds, they can be optically active as well. $\endgroup$ – Mathew Mahindaratne Aug 19 '20 at 17:15
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Quoting your source itself:

An object that is chiral is an object that can not be superimposed on its mirror image.

Let's think about this a little bit:
If we have a single carbon atom bonded to four completely different groups (be it functional or alkyl) we will achieve non-superimposability:

chiral molecule

(Try re-drawing the structures replacing the $\ce{-COOH}$ group with $\ce{-C2H5}$ and check if you can achieve superimposability)

Achieving non-superimposability is all that optical isomerism is about. As long as we cannot superimpose the object on its mirror image, and can find no symmetrical elements, we can confidently declare that particular compound to be optically active.

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