Understanding the Problem

We are given the dipole moment and bond length of a diatomic molecule and we need to calculate the charge fraction on each atom. To solve this problem, we can use the concept of dipole moment and the relationship between charge and dipole moment.

Calculating Charge Fraction

The dipole moment (\( \mu \)) of a molecule is given by the product of the charge (\( q \)) and the distance of separation (\( r \)) between the charges:

\( \mu = q \cdot r \)

In this case, we are given the dipole moment (\( \mu = 1.2 \) D) and the bond length (\( r = 1 \) Å). We need to find the charge fraction (\( \frac{q}{e} \)) on each atom.

Here, \( e \) is the elementary charge, which is the charge of a proton or an electron. It is approximately \( 1.602 \times 10^{-19} \) C.

We can rearrange the equation for dipole moment to solve for \( q \):

\( q = \frac{\mu}{r} \)

Substituting the given values, we have:

\( q = \frac{1.2 \, \text{D}}{1 \, \text{Å}} = 1.2 \, \text{D} \times \frac{1 \, \text{Å}}{1 \, \text{D}} = 1.2 \, \text{Å} \)

Now, we need to calculate the charge fraction (\( \frac{q}{e} \)) on each atom. Let's assume that the charge on one atom is \( x \) and the charge on the other atom is \( y \). Since the molecule is neutral overall, the sum of the charges on each atom should be zero.

\( x + y = 0 \)

From the given information, we know that \( q = 1.2 \, \text{Å} \). Therefore, we can write:

\( x = \frac{q}{e} \) and \( y = -\frac{q}{e} \)

Substituting the values, we have:

\( x = \frac{1.2 \, \text{Å}}{1.602 \times 10^{-19} \, \text{C}} \) and \( y = -\frac{1.2 \, \text{Å}}{1.602 \times 10^{-19} \, \text{C}} \)

Calculating these values, we find:

\( x \approx 7.48 \times 10^{18} \) and \( y \approx -7.48 \times 10^{18} \)

The charge fraction on each atom can be calculated as a percentage of the elementary charge:

\( \text{Charge fraction on each atom} = \frac{q}{e} \times 100 \)

Substituting the values, we get:

\( \text{Charge fraction on each atom} = \frac{7.48 \times 10^{18}}{1.602 \times 10^{-19}} \times 100 \)

Simplifying this expression, we find:

\( \text