Question

A diatomic molecule has a dipole moment of $ 4 \times 10^{-30} \, \text{Cm} $. If the bond distance is $ 1.0 \, \text{\AA} $, what fraction of an electronic charge exists on each atom? (Actual value of electronic charge = $ 1.6 \times 10^{-19} \, \text{C} $)

• A. $ 0.33 $
• B. $ 0.50 $
• C. $ 0.25 $
• D. $ 0.66 $

Hint:

To calculate the fraction of electronic charge: 1. Use the dipole moment formula: $ \mu = q \cdot d $. 2. Solve for $ q $ and divide by the electronic charge ($ e $).

Answer 1

The Correct Option is C

\textbf{Step 1: Recall the Formula for Dipole Moment} The dipole moment ($ \mu $) of a diatomic molecule is given by: $$ \mu = q \cdot d $$ where:
$ q $ is the magnitude of the charge separation,
$ d $ is the bond distance.
Rearranging for $ q $: $$ q = \frac{\mu}{d} $$ Step 2: Substitute Given Values Dipole moment ($ \mu $): $ 4 \times 10^{-30} \, \text{Cm} $
Bond distance ($ d $): $ 1.0 \, \text{\AA} = 1.0 \times 10^{-10} \, \text{m} $
Substitute these values into the formula: $$ q = \frac{4 \times 10^{-30}}{1.0 \times 10^{-10}} $$ $$ q = 4 \times 10^{-20} \, \text{C} $$ Step 3: Determine the Fraction of Electronic Charge
The actual value of the electronic charge ($ e $) is: $$ e = 1.6 \times 10^{-19} \, \text{C} $$ The fraction of the electronic charge on each atom is: $$ \text{Fraction} = \frac{q}{e} $$ Substitute $ q = 4 \times 10^{-20} \, \text{C} $ and $ e = 1.6 \times 10^{-19} \, \text{C} $: $$ \text{Fraction} = \frac{4 \times 10^{-20}}{1.6 \times 10^{-19}} $$ $$ \text{Fraction} = \frac{4}{16} = 0.25 $$ Step 4: Analyze the Options
Option (1): $ 0.33 $
Incorrect — does not match the calculated value. Option (2): $ 0.50 $
Incorrect — does not match the calculated value. Option (3): $ 0.25 $
Correct — matches the calculated value. Option (4): $ 0.66 $
Incorrect — does not match the calculated value.