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?
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?
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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.
Updated On: Apr 7, 2026
- \( [r_A + r_B] : [2(r_A + r_B)] \)
- \( [r_A + r_B] : [(r_A + r_B)] \)
- \( \left[\frac{1}{2}(r_A + r_B)\right] : [(r_A + r_B)] \)
- \( \left[\frac{1}{2}(r_A + r_B)\right] : [2(r_A + r_B)] \)
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The Correct Option is A
Solution and Explanation
Step 1: Understanding bond length and total length of a molecule.
When two elements A and B are covalently bonded, the bond length between them is typically the sum of their individual atomic radii. This is represented as: \[ \text{Bond length} = r_A + r_B \] This is the distance between the nuclei of the two atoms involved in the bond.
The total length of the molecule, however, depends on the geometry of the molecule. For example, in a linear molecule, the total length is often twice the bond length (for molecules consisting of two atoms), and this is commonly expressed as: \[ \text{Total length} = 2(r_A + r_B) \]
Step 2: Analyzing the options.
- Option (A) is correct because the bond length is \( r_A + r_B \), and the total length for a simple diatomic molecule is \( 2(r_A + r_B) \). Therefore, the correct relationship between bond length and total length is: \[ \text{Bond length} : \text{Total length} = [r_A + r_B] : [2(r_A + r_B)] \] - Option (B) is incorrect because the total length should not be equal to the bond length in a typical diatomic molecule. - Option (C) is incorrect because it suggests a fraction for the bond length, which is not generally applicable for covalent bonds between two atoms. - Option (D) is also incorrect because the bond length and total length are not related by such a ratio. Thus, the correct option is (A).
Final Answer: \( [r_A + r_B] : [2(r_A + r_B)] \).
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