I am confused about how they have named the above compound.
How are they assigning R stereochemistry to this molecule? Aren't the two carbons achiral?
For numbering, how to know which substituent has priority? I mean ethyl is 1 and isopropyl is 4?
No, they both have four substituents. They would be achiral if C-1 and C-4 BOTH had an ethyl or BOTH had an isopropyl--making the molecule symmetric-- but they don't, hence the chirality.
I actually don't think those are chiral carbons, the mirror image of this molecule is identical. And if you trace going around, each path inevitably leads to the same CIP for the ring carbons. You cant have two identical R groups on a chiral carbon as assigning R/S would be literally impossible. I think that is a typo or they pulled the image from some weird source, even the IUPAC name is missing the R/S designation in the name.
There are 2 carbons between each group, this makes the whole structure symmetrical. Essentially, two of your R groups are going to have the same number of carbons going each way around the ring, ending at the ethyl or isopropyl group, so how would you decide between one vs the other if the CIP for each is identical because there is no point of first difference. if the groups were shifted one carbon left or right then yes, they would both be chiral. But I can see a plane of symmetry down the middle.The bottom side chain has isopropyl and is attached at C2. The top side chain is an ethyl group. So, I think that's why they are chiral carbons, since each of them have 4 different substituents attached.