To understand why the minimum number of carbon atoms of an alkane must be 4 to form an isomer, let's first define what isomers are and how they relate to alkane molecules.

Isomers are compounds that have the same molecular formula but different structural arrangements. In other words, they have the same number and types of atoms but differ in the way these atoms are connected to each other. Isomerism is particularly prevalent in organic chemistry, where carbon atoms can form diverse and complex structures.

Alkanes are saturated hydrocarbons consisting of carbon and hydrogen atoms, with the general formula CnH2n+2. The carbon atoms in alkanes are connected to each other in a linear or branched chain. When the number of carbon atoms is increased, the potential for isomerism also increases.

Now, let's examine the options given:

a) 4 carbon atoms
b) 3 carbon atoms
c) 2 carbon atoms
d) 1 carbon atom

Explanation:

1. 1 carbon atom (option d):
A single carbon atom cannot form an isomer because there is no possibility of rearranging the atoms or changing the structure.

2. 2 carbon atoms (option c):
With two carbon atoms, only one possible arrangement is possible, which is a straight chain. Thus, there are no isomers in this case.

3. 3 carbon atoms (option b):
With three carbon atoms, two isomers are possible. These are known as propene and cyclopropane. However, it is important to note that propene is an alkene and not an alkane.

4. 4 carbon atoms (option a):
When we have four carbon atoms, isomerism becomes possible. The two main structural isomers of butane are n-butane and isobutane. n-butane has a linear chain of carbon atoms, while isobutane has a branched structure.

n-butane: CH3-CH2-CH2-CH3
isobutane: CH3-CH(CH3)-CH3

These isomers have different physical and chemical properties due to their different structures.

Conclusion:

In summary, the minimum number of carbon atoms required for an alkane to have isomers is four (option a). This is because with four carbon atoms, different structural arrangements and branching patterns become possible, leading to the formation of isomers.

An Alkane with 4 carbon atoms forms only two isomers :- 1) n-butane & 2)iso-butane
Remaining options does not forms any isomers..