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Lewis Dot Structure

If A-BBond ...

Question

If $(A - B)_{B o n d l e n g t h} = 1.32 A^{o}$ ; $(A - A)_{B o n d l e n g t h} = 2 A^{o}$ ; $(B - B)_{B o n d l e n g t h} = 1 A^{o}$ the % covalent character of A-B bond can be expressed as (10x + y)% (where x and y varies from 0-9) then value of $\sqrt{x^{2} - y^{2}} = ?$

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Solution

$(A - B)$ Bond length = $1.32 ˚ A$
$(B - B)$ Bond length = $1 ˚ A$
$(A - A)$ Bond length = $2 ˚ A$
Atomic radius of $A = 1 ˚ A$
Atomic radius of $B = 0.5 ˚ A$
Observed bond length = $1.32 ˚ A$
Calculated bond length of $A - B = 1 ˚ A + 0.5 ˚ A = 1.5 ˚ A$
$%$ covalent character = $\frac{1.32}{1.5} \times 100$
$= 88 %$
$10 x + y = 88 %$
$x = 8 y = 8$
$= \sqrt{x^{2} - y^{2}} = 0$

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