How many chiral carbon atoms are present in $\mathrm{\beta }$ -D-ribose?

In straight-chain D-ribose, an aldopentose, carbons C2, C3, and C4 are stereogenic; C1 is the aldehyde carbonyl (achiral) and C5 is CH₂OH (achiral). When D-ribose cyclizes to the furanose form, it forms a hemiacetal at C1. That new tetrahedral center becomes stereogenic, and its configuration defines the anomer: β when the anomeric OH is on the same side as the CH₂OH group in the Haworth view for a D-sugar.

So β-D-ribofuranose has four chiral carbons in total: C1, C2, C3, and C4. The α and β anomers interconvert in solution (mutarotation), but in the β anomer specifically, all four of those centers are chiral.