Define Covalent Radius and Metallic Radius.

📚 Chapter: Classification of Elements and Periodicity in Properties

📘 Detailed Solution

🔵 1. Covalent Radius

The covalent radius of an atom is defined as half the distance between the nuclei of two identical atoms joined by a single covalent bond.

Covalent Radius = ½ × Internuclear Distance

Atom
A — Atom
A

If the distance between the nuclei of two bonded identical atoms is d, then:

r_c = d / 2

Example: In an H₂ molecule, the distance between the nuclei of the two hydrogen atoms is approximately twice the covalent radius of hydrogen.

🟣 2. Metallic Radius

The metallic radius of an atom is defined as half the distance between the nuclei of two adjacent metal atoms in a metallic crystal.

Metallic Radius = ½ × Distance between adjacent metal nuclei

M — M

If the distance between the nuclei of two adjacent metal atoms is d, then:

r_m = d / 2

The metallic radius is generally used to describe the size of atoms in a metallic crystal lattice.

🟢 Difference Between Covalent and Metallic Radius

Basis	Covalent Radius	Metallic Radius
Meaning	Half the distance between nuclei of two identical covalently bonded atoms	Half the distance between nuclei of two adjacent metal atoms
Found in	Covalent molecules	Metallic crystals
Bond/Arrangement	Covalent bond	Metallic lattice
Symbol	rc	rm

🎬 Radius Concept

Covalent Radius

A ← r → • ← r → A

Total distance = 2r

↓

Radius = Half of internuclear distance

✅ Final Answer

Covalent Radius: It is half the distance between the nuclei of two identical atoms joined by a single covalent bond.

Metallic Radius: It is half the distance between the nuclei of two adjacent metal atoms in a metallic crystal.

r_c = ½ × internuclear distance
r_m = ½ × distance between adjacent metal atoms

📝 20 MCQs with Answers

1. Covalent radius is defined as:

A) Distance between two atoms

B) Half the distance between nuclei of two identical covalently bonded atoms

C) Diameter of an atom

D) Distance between electrons

✅ Answer

B) Half the distance between nuclei of two identical covalently bonded atoms.

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2. Metallic radius is measured in:

A) Ionic molecules

B) Metallic crystals

C) Covalent molecules only

D) Gases only

✅ Answer

B) Metallic crystals

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3. Covalent radius is equal to:

A) d

B) 2d

C) d/2

D) d²

✅ Answer

C) d/2

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4. Metallic radius is equal to:

A) d/2

B) 2d

C) d²

D) d+2

✅ Answer

A) d/2

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5. Covalent radius is associated with:

A) Covalent bond

B) Ionic bond only

C) Metallic bond only

D) Hydrogen bond only

✅ Answer

A) Covalent bond

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6. Metallic radius refers to the size of atoms in:

A) Metallic lattice

B) Water

C) Gas molecules

D) Ionic solution

✅ Answer

A) Metallic lattice

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7. The distance used to determine covalent radius is between:

A) Electron and nucleus

B) Nuclei of bonded atoms

C) Two electrons

D) Two ions in solution

✅ Answer

B) Nuclei of bonded atoms

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8. The distance used to determine metallic radius is between:

A) Nuclei of adjacent metal atoms

B) Electrons only

C) Ions in solution

D) Nucleus and electron

✅ Answer

A) Nuclei of adjacent metal atoms

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9. If internuclear distance in a covalent molecule is 200 pm, its covalent radius is:

A) 50 pm

B) 100 pm

C) 200 pm

D) 400 pm

✅ Answer

B) 100 pm

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10. If adjacent metal nuclei are 300 pm apart, metallic radius is:

A) 50 pm

B) 100 pm

C) 150 pm

D) 300 pm

✅ Answer

C) 150 pm

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11. Covalent radius is generally used for:

A) Covalently bonded atoms

B) Free electrons

C) Metallic ions only

D) Neutrons

✅ Answer

A) Covalently bonded atoms

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12. Metallic radius is generally used for:

A) Metal atoms in a crystal

B) Non-metal molecules only

C) Noble gases only

D) Anions only

✅ Answer

A) Metal atoms in a crystal

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13. Which radius is based on half the internuclear distance?

A) Covalent radius

B) Both covalent and metallic radius

C) Only ionic radius

D) Nuclear radius

✅ Answer

B) Both covalent and metallic radius

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14. The symbol commonly used for covalent radius is:

A) r_c

B) r_m

C) r_i

D) R_g

✅ Answer

A) r_c

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15. The symbol commonly used for metallic radius is:

A) r_c

B) r_m

C) r_i

D) r_a

✅ Answer

B) r_m

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16. Which statement is correct?

A) Covalent radius is half the internuclear distance in a covalent bond

B) Covalent radius is always the full internuclear distance

C) Metallic radius is measured between electrons

D) Metallic radius is the diameter of a metal atom

✅ Answer

A) Covalent radius is half the internuclear distance in a covalent bond.

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17. Metallic radius is especially useful for describing:

A) Crystal structure of metals

B) Molecular mass

C) Boiling point only

D) Atomic number

✅ Answer

A) Crystal structure of metals

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18. Which one involves identical atoms?

A) Standard covalent radius determination

B) Metallic radius determination

C) Both definitions can involve identical neighbouring atoms

D) Neither

✅ Answer

C) Both definitions can involve identical neighbouring atoms.

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19. If metallic radius is 125 pm, distance between adjacent nuclei is:

A) 62.5 pm

B) 125 pm

C) 250 pm

D) 500 pm

✅ Answer

C) 250 pm

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20. Which pair is correctly matched?

A) Covalent radius — metallic crystal

B) Metallic radius — covalent molecule

C) Covalent radius — covalent bond

D) Both — electron radius

✅ Answer

C) Covalent radius — covalent bond

Q1. Define covalent radius.

Solution: Covalent radius is half the distance between the nuclei of two identical atoms joined by a single covalent bond.

Q2. Define metallic radius.

Solution: Metallic radius is half the distance between the nuclei of two adjacent metal atoms in a metallic crystal.

Q1. Differentiate between covalent radius and metallic radius.

Covalent Radius	Metallic Radius
Used for covalently bonded atoms	Used for atoms in metallic crystals
Half the internuclear distance of bonded atoms	Half the distance between adjacent metal nuclei
Associated with covalent bonding	Associated with metallic crystal arrangement

Q1. Explain covalent radius and metallic radius with mathematical expressions.

Solution:

For two identical covalently bonded atoms separated by distance d:

r_c = d/2

For two adjacent metal atoms separated by distance d:

r_m = d/2

Thus, in both cases the radius is obtained by taking half the appropriate distance between the two nuclei.

Q1. Explain different types of atomic radius with special reference to covalent and metallic radius.

Solution:

• Covalent radius: Half the internuclear distance between two identical covalently bonded atoms.
• Metallic radius: Half the distance between the nuclei of two adjacent atoms in a metallic crystal.
• Both are measures of atomic size under different bonding or structural conditions.
• Covalent radius is used mainly for covalent compounds.
• Metallic radius is used for metals in their crystal structures.

Key Point:
Atomic radius depends on the chemical environment in which an atom is present.

Q1. Define covalent and metallic radius. Explain their determination with suitable diagrams and formulae.

Solution:

Atomic size cannot be determined as an absolute boundary because the electron cloud of an atom does not have a sharply defined outer edge. Therefore, different operational definitions of atomic radius are used.

1. Covalent Radius

When two identical atoms are joined by a single covalent bond, the covalent radius is taken as half the distance between their nuclei.

r_c = ½ × internuclear distance

A — d — A

Therefore, d = 2r_c.

2. Metallic Radius

In a metallic crystal, the metallic radius is taken as half the distance between the nuclei of two adjacent metal atoms.

r_m = ½ × distance between adjacent nuclei

M — d — M

The metallic radius is therefore a useful measure of atomic size in a metallic crystal lattice.

Point	Covalent Radius	Metallic Radius
System	Covalent molecule	Metallic crystal
Measurement	½ internuclear distance	½ distance between adjacent metal nuclei
Association	Covalent bond	Metallic lattice

🎯 Final Answer:

Covalent Radius: Half the distance between the nuclei of two identical atoms joined by a single covalent bond.

Metallic Radius: Half the distance between the nuclei of two adjacent metal atoms in a metallic crystal.

🎯 Quick Revision

Covalent Radius → ½ × internuclear distance
Metallic Radius → ½ × distance between adjacent metal nuclei
Covalent Radius → Covalent bond
Metallic Radius → Metallic crystal
Both → Measures of atomic size