Which of the following can show optical isomerism? (a) 2-bromo-2-chlorobutane (b) 2 -methylpropane (c) 2,2-dimethyl-1-butanol (d) 2,2,4-trimethylpentane

In each compound, we need to find the carbon atom having four different atoms or groups attached to it, which is a chiral center. (a) 2-bromo-2-chlorobutane: Structure - CH3CHBrCHClCH3 The second carbon (C2) has four different groups attached: -H, -CH3, -Br, and -Cl. So, it is a chiral center. (b) 2-methylpropane: Structure - (CH3)3CH The second carbon (C2) has only three different groups attached: -H and three -CH3. So, it doesn't have a chiral center. (c) 2,2-dimethyl-1-butanol: Structure - HOC(CH3)C(CH3)2CH2CH3 The second carbon (C2) has only three different groups attached: -OH, -CH3, and an -isopropyl group. So, it doesn't have a chiral center. (d) 2,2,4-trimethylpentane: Structure - (CH3)3CCH2CH(CH3)2 There are no carbons with four different groups attached, just carbons that have either -H, two -CH3, or three -CH3 attached. So, it doesn't have a chiral center.

The compound with a chiral center is 2-bromo-2-chlorobutane. Since it has a chiral center, it can show optical isomerism. So, the answer is (a) 2-bromo-2-chlorobutane.