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  Calculation of Atomic Radius

Calculation of Atomic Radius (Covalent Radius):

Atomic radius is the total distance from centre of the nucleus to the point where electron density is efficiently zero.

A. Homonuclear diatomic molecules:

In situation of homonuclear diatomic molecules of A2 type (example, F2, Cl2, Br2, I2... etc.) the bond length, d (A-A) is specified by,

d(A – A) = r(A) + r(A)
d(A – A) = 2 × r(A)
r(A) = [d(A–A)]/ 2
             
The above equation shows that in the condition of homonuclear diatomic molecule of A2 type, the covalent radius of an atom A, r(A) is equivalent to one half of the inter-nuclear distance, d(A-A). Thus, the covalent radius of an atom in a homonuclear diatomic molecule can be acquired by dividing the internuclear distance by two.

Illustration:

Cl2 molecule:

The value of Cl–Cl bond distance as determine experimentally is 1.98Å. Therefore
r(Cl) = d(Cl–Cl)/2 = 1.98/2 = 0.99Å

Diamond:

The value of d(C–C) distance as determine experimentally in a diversity of saturated hydrocarbons is 1.54Å.
r(C) = d(C–C)/2 = 1.54/2 = 0.77Å

B. Heteronuclear diatomic molecule:

In situation of heteronuclear diatomic molecule of AB type, the bond length d (A – B) is specified by,

d(A – B) = r(A) + r(B)
r(A) and r(B) are the covalent radii of A & B atoms.

Illustration:

CCl4 molecule:

The experimental value of d(C – Cl) is 1.76 Å
Therefore d(C–Cl) = r(C) + r(Cl)
r(C) = d(C – Cl) – r(Cl)
= 1.76 – r(Cl)

Therefore the covalent radius of carbon atom can be computed by subtracting the covalent radius of Cl atom from d(C–Cl) bond length. The covalent radius of Cl atom can as well be acquired, given that covalent radius of C atom is recognized.

SiC:

The experimental value of d (Si-C) is 1.93 Å. Therefore,

d(Si – C) = r(Si) + r(C)
r(Si) = d(Si – C) – r(C)
= 1.93 – r(C)
= 1.93 – 0.77 [since, r(C) = 0.77 Å]
= 1.16 Å

 

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