Nucleophilic substitution is the correct answer for the reaction of sodium ethoxide with ethyl iodide to form diethyl ether.

Nucleophilic substitution reactions involve the replacement of a leaving group with a nucleophile. In this case, the ethoxide ion (C2H5O-) acts as the nucleophile and replaces the iodide ion as the leaving group.

Here is a detailed explanation of why nucleophilic substitution is the correct term for this reaction:

1. Nucleophile Attack:
- Sodium ethoxide (C2H5ONa) is a strong nucleophile. It has a lone pair of electrons on the oxygen atom, making it an excellent nucleophile.
- Ethyl iodide (C2H5I) is an alkyl halide with a good leaving group, iodide ion (I-), which readily dissociates in solution.
- In the reaction, the nucleophile attacks the carbon atom of the ethyl iodide, displacing the iodide ion. The oxygen atom of the nucleophile donates its lone pair of electrons to form a new bond with the carbon atom, resulting in the formation of an ether molecule.
- The reaction can be represented as follows:
C2H5ONa + C2H5I → C2H5OC2H5 + NaI

2. Leaving Group:
- The iodide ion (I-) is a good leaving group because it is relatively stable and can easily dissociate from the carbon atom.
- As the nucleophile attacks, the iodide ion leaves the carbon atom, resulting in the formation of sodium iodide (NaI) as a byproduct.

3. Solvent:
- The reaction typically takes place in an aprotic solvent, such as an ether or a polar aprotic solvent like dimethyl sulfoxide (DMSO).
- These solvents do not have acidic hydrogens and do not undergo nucleophilic substitution themselves.

4. Mechanism:
- The reaction proceeds through an SN2 (substitution nucleophilic bimolecular) mechanism, where the nucleophile attacks the carbon atom from the backside, resulting in the inversion of configuration.
- The SN2 mechanism involves a single step transition state, in which the nucleophile and the leaving group are both involved.

In conclusion, the reaction of sodium ethoxide with ethyl iodide to form diethyl ether is a nucleophilic substitution reaction. The strong nucleophile, sodium ethoxide, attacks the carbon atom of ethyl iodide, replacing the iodide ion as the leaving group. This reaction follows the SN2 mechanism and leads to the formation of diethyl ether and sodium iodide as the byproduct.