A gaseous diatomic molecule HX has an observed dipole moment of 1.08 D and its bond is 16.4% ionic. Taking percent ionic character =100xmu_obs/(e d) with e=1.6x10^-19 C and 1 D=3.336x10^-30 C m, calculate the bond length d in pm (nearest integer).

JEE Advanced levelNumerical answerDifficulty 3 of 3cb210

A gaseous diatomic molecule $HX$ has an observed dipole moment of $1.08 D$ and its bond is $16.4%$ ionic. Taking percent ionic character $= 100 \times μ_{o b s} / (e d)$ with $e = 1.6 \times 1 0^{- 19} C$ and $1 D = 3.336 \times 1 0^{- 30} C m$ , calculate the bond length $d$ in pm (nearest integer).

Numerical answer type, answer in pm, tolerance 0.5.

μ_{i o ni c} = μ_{o b s} / fraction ionic = 1.08/0.164 = 6.585 D = 2.197 e - 29 C m

. Then

d = μ_{i o ni c} / e = 2.197 e - 29/1.6 \times 1 0^{- 19}

, which gives

d = 1.373 e - 10 m \approx 137.3 pm

, i.e. 137 pm.