Alpha Carbon Beta Carbon and Gamma Carbon Organic Chemistry:

Alpha Carbon	Beta Carbon	Gamma Carbon
The carbon atom to which the functional group is attached directly in an organic compound is known as alpha (α) carbon.	Carbon next attached directly to alpha carbon in an organic compound is known as beta (β) carbon.	Carbon next attached directly to beta carbon in an organic compound is known as gamma (γ) carbon.

Example of Alpha Carbon Beta Carbon and Gamma Carbon :

Identify Alpha Carbon Beta Carbon and Gamma Carbon and hydrogens:

Example 1:

Example 2:

Example 3:

Alpha carbon in alkene:

For example, no.1, the carbon that is attached to the unsaturated system is the alpha carbon in alkene and the hydrogens attached to the alpha carbon are alpha hydrogens.

In example no.2, there are two functional groups (-CHO) and (-Cl) so there are two alpha carbons and the hydrogen attached directly to the alpha carbon are alpha hydrogens.
The carbon atom next to alpha carbon is a beta carbon and the hydrogens attached to beta carbon are beta hydrogens.

In example no.3, OH is a functional group attached to bond line notation and the carbon atom attached directly to the functional group is an alpha carbon.
After alpha carbon is next attached directly to carbon is beta carbon and then gamma (γ) carbon in an organic compound.