To find the fractional charge on each atom in a diatomic molecule, we can use the relationship between dipole moment (μ), charge (q), and distance (d):

$$ \mu = q \times d $$

Where:

• μ is the dipole moment.


• q is the magnitude of the charge on each atom.


• d is the distance between the charges.

First, convert units to be consistent with esu:

• Bond distance in cm: $$ 1 \mathrm{~A}^{\circ} = 1 \times 10^{-8} \mathrm{~cm} $$


• Dipole moment in esu·cm: $$ 1.2 \mathrm{~D} = 1.2 \times 10^{-18} \mathrm{~esucm} $$

We are given that the bond distance ($ d $) is $ 1 \mathrm{~A}^{\circ} $ and that the dipole moment $( \mu $) is $ 1.2 \mathrm{~D} $. Using these values, we can calculate the charge ($ q $) as follows:

$$ q = \frac{\mu}{d} $$

Now plug in the given values:

$$ q = \frac{1.2 \times 10^{-18} \mathrm{~esucm}}{1 \times 10^{-8} \mathrm{~cm}} $$

$$ q = 1.2 \times 10^{-10} \mathrm{~esu} $$

$$ q = 1.2 \times 10^{-9} \times 10^{-1} \mathrm{~esu} $$

$$ q = 0.000000012 \times 10^{-1} \mathrm{~esu} $$