Question

If \( r_A \) and \( r_B \) are the radii of elements A and B respectively. Element A and B are covalently bonded. What will be the bond length and total length of the molecule?

• A. \( [r_A + r_B] : [2(r_A + r_B)] \)
• B. \( [r_A + r_B] : [(r_A + r_B)] \)
• C. \( \left[\frac{1}{2}(r_A + r_B)\right] : [(r_A + r_B)] \)
• D. \( \left[\frac{1}{2}(r_A + r_B)\right] : [2(r_A + r_B)] \)

Hint:

For a simple covalent molecule consisting of two atoms A and B, the bond length is the sum of the atomic radii \( r_A + r_B \), and the total length of the molecule is typically twice the bond length in a linear molecule.

Answer 1

The Correct Option is A

Step 1: Understanding the Concept: 
For a covalent bond between two different atoms A and B, the bond length is defined as the internuclear distance -- the distance between the centers (nuclei) of the two bonded atoms. 
The total molecular length (or overall span) is the distance from the outermost edge of atom A to the outermost edge of atom B, measured along the bond axis. 
Step 2: Detailed Explanation: 
Bond Length: 
If we model each atom as a sphere, the center of atom A is at radius \(r_A\) from its surface, and the center of atom B is at radius \(r_B\) from its surface. 
When covalently bonded, their surfaces touch (or overlap), so the distance between nuclei is approximately: 
\[ d_{AB} = r_A + r_B \] 
Total Molecular Length: 
The molecule extends from the far edge of atom A to the far edge of atom B. 
Starting from the outer surface of A: we travel through the radius of A (\(r_A\)) to reach nucleus A, then through the bond (\(r_A + r_B\)) to reach nucleus B, then through the radius of B (\(r_B\)) to reach the outer edge of B. 
Total length = \(r_A + (r_A + r_B) + r_B = 2r_A + 2r_B = 2(r_A + r_B)\). 
Alternatively, the total length represents the diameter of the full molecular system: 
\[ \text{Total Length} = 2(r_A + r_B) \] 
Step 3: Final Answer: 
Bond length = \(r_A + r_B\);    Total length = \(2(r_A + r_B)\).