A correct name for the following compound is:.a) 4-bromo-3,8-dimethylbicyclo[5.2.2]n onane b) 3,8-dimethyl-4-bromo-bicyclo[5.2.O) nonane c) 4-bromo-3,8-dimethylbicyclo[5.2.1]d ecane d) 7-bromo-2,6-dimethylbicyclo[5.2.0]n onane e) 4-bromo-3,8-dimethylbicyclo[5.2.0]n onane

e) 4-bromo-3,8-dimethylbicyclo[5.2.0]nonane

Explanation:

The missing image of the the  compound we are to name is attached below.

Before we can name an organic compound; It is crucial we know the guiding rules in naming them.

1. Select the longest continuous carbon chain as the root hydrocarbon and name according to the number of carbon atoms it contains, adding appropriate suffix to indicate the principal substituent group.

2. Number the carbon atoms in the root hydrocarbon from the end which gives the lowest number to the substituents.

3. If the same substituent is present two  or more times  in a molecule; the number of this substituent is indicated by the prefix di -(2), tri - (3) , tetra - (4) etc attached to the substituent name.

4. If there is more than one type of substituent in the molecule ; the substituents are named according to the alphabetical order but where  there are mixed substituents ; the inorganic are named first.

5. In selecting and numbering the longest continuous chain, the functional groups are given preference over substituents., i.e the functional group is given the smallest possible number.

In the light of the above guiding rules; we were able to name the given compound because the compound contains nine carbons in the ring form which result to root name nonane. The two methyl are on the third and eight carbon; bromine is on the fourth carbon ; there are two cyclic ring present in the compound where we have 5 carbons in one structure, another 2 carbons in the second structure and zero carbon in the bridge structure which eventually result to the correct  name:

4-bromo-3,8-dimethylbicyclo[5.2.0]nonane