To find whether an atom in an organic molecule is chiral or achiral use the following flow chart.
If two or more ligands on a tetrahedral atom in a molecule form a ring, to determine whether they are different or not, use the following procedure.
Two of the ligands on C-1 in 1 are a hydrogen atom and a methyl group. The other two ligands form a ring. To determine whether they are identical or not, convert them to two hypothetical ligands:
Step 1: Number the rest of the carbon atoms in the ring for identification purposes in any way you wish.
Step 2: Break the bond connecting C-1 and C-6.
Step 3: The bond broken in Step 2 connected C-6 to a carbon atom (C-1). Therefore, connect C-6 to a C atom that bears no ligands.
Step 4: Break the bond connecting C-1 and C-2 in 1.
Step 5: The bond broken in Step 4 connected C-2 to a carbon atom (C-1). Therefore, connect C-2 to a C atom that bears no ligands.
Hypothetically, the four ligands on C-1 in 1 are as follow.
Notice that the two ligands that form the ring are identical. Thus, the four ligands on C-1 in 1 are not different.
i. The chiral centers are marked with a red asterisk.
ii. The chiral centers are marked with a red asterisk.