The table given below lists the bond dissociation energy `(E_("diss"))` for single covalent bonds formed between C and atoms A, B, D, E.
`{:("Bond",,,E_("diss")("kcal mol"^(-1))),(C-A,,," "240),(C-B,,," "382),(C-D,,," "276),(C-E,,," "486):}`
Which of the atoms has smallest size ?

Options

A. D
B. E
C. A
D. D

Explanation

To determine which atom has the smallest size based on the given bond dissociation energies, we can follow these steps:

### Step 1: Understand Bond Dissociation Energy
Bond dissociation energy (E_diss) is the energy required to break a bond between two atoms. A higher bond dissociation energy indicates a stronger bond, which typically corresponds to a shorter bond length.

### Step 2: Analyze the Given Data
The bond dissociation energies for the bonds between carbon (C) and the atoms A, B, D, and E are as follows:
- C-A: 240 kcal/mol
- C-B: 382 kcal/mol
- C-D: 276 kcal/mol
- C-E: 486 kcal/mol

### Step 3: Compare the Bond Dissociation Energies
From the data:
- C-E has the highest bond dissociation energy (486 kcal/mol).
- C-B has the second highest (382 kcal/mol).
- C-D has a lower value (276 kcal/mol).
- C-A has the lowest value (240 kcal/mol).

### Step 4: Relate Bond Strength to Atomic Size
As stated, bond dissociation energy is inversely related to atomic size:
- Higher bond dissociation energy → Stronger bond → Smaller atomic size
- Lower bond dissociation energy → Weaker bond → Larger atomic size

### Step 5: Identify the Atom with the Smallest Size
Since C-E has the highest bond dissociation energy, it indicates that the bond is strong and the size of atom E is the smallest among the given atoms.

### Conclusion
Therefore, the atom with the smallest size is **E**.

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