\(\alpha\) - and \(\beta\) -glucose differ in the orientation of \(-\mathrm{OH}\) group around (a) \(\mathrm{C}_{1}\) (b) \(\mathrm{C}_{2}\) (c) \(\mathrm{C}_{3}\) (d) \(\mathrm{C}_{4}\)

Stereosiomerism is a form of isomerism where molecules have the same molecular formula and sequence of bonded atoms (constitution), but differ in the three-dimensional orientations of their atoms in space. This concept becomes particularly important when we talk about carbohydrates like glucose, which can exist in several stereoisomeric forms.

In the case of glucose, stereoisomerism is observed due to the existence of multiple chiral centers – carbon atoms attached to four different groups. When glucose forms a ring structure, a new stereocenter is created at the carbon which was part of the carbonyl group in the open-chain form. This leads to the formation of two isomers, known as anomers, which differ in the position of the hydroxyl group at the anomeric carbon after the ring closure occurs. Understanding this concept allows one to grasp why glucose can exist in different forms such as α-glucose and β-glucose, which are not just important in chemistry but are also biologically significant.

The anomeric carbon in a sugar molecule is a central concept in carbohydrate chemistry. It is the carbon derived from the carbonyl (aldehyde or ketone) group of the open-chain form, which becomes the chiral center upon cyclic ring formation. In glucose, this is the carbon number 1 (C1).

During the process of cyclization, the hydroxyl group (-OH) attached to the anomeric carbon can have two different spatial orientations: axial (pointing downward) in the α-anomer, or equatorial (pointing upward) in the β-anomer. The distinction between these two configurations is crucial because it influences how the sugar interacts with other molecules, including how it binds to enzymes and how it is recognized by other biological molecules. Therefore, this particular carbon not only defines the anomer but also plays an essential role in the biochemical behavior and functionality of the sugar.

Haworth projection is a common method used to represent the cyclic structure of sugars such as glucose in a way that is easier to visualize and understand. This technique simplifies the three-dimensional ring structure by flattening it onto a two-dimensional plane.

The projection shows the ring form of a carbohydrate, with the more substituted side of the ring drawn as a flat line and the less substituted side as a vertical line. Hydroxyl groups and other substituents are then added, pointing either above or below the plane of the ring to indicate their stereochemical orientation.

In the context of glucose, the Haworth projection is especially useful to distinguish between the α- and β-anomers. By convention, if the hydroxyl group on the anomeric carbon is on the right side of the molecule in a Fischer projection, it will point down in an α-Haworth projection and up in a β-Haworth projection. These visual clues provided by the Haworth projection are invaluable for students and chemists alike when it comes to understanding and predicting the reactivity and interactions of different sugar molecules.