Question

For the following question, enter the correct numerical value up to TWO decimal places. If the numerical value has more than two decimal places, round-off the value to TWO decimal places. (For example: Numerical value 5 will be written as 5.00 and 2.346 will be written as 2.35) A diatomic molecule has a dipole moment of \(1.2\,\text{D}\). If the bond distance is \(1.0\,\text{\AA}\), the fraction of an electronic charge on each atom is _____

Hint:

For dipole moment problems, always convert Debye to SI units before calculation.

Answer 1

Correct Answer: 0.25

Step 1: Dipole moment is given by \[ \mu = qd \] where \( q \) is the charge and \( d \) is the separation.
Step 2: Convert dipole moment into SI units: \[ 1\,\text{D} = 3.336 \times 10^{-30}\,\text{C m} \] \[ \mu = 1.2 \times 3.336 \times 10^{-30} = 4.003 \times 10^{-30}\,\text{C m} \]
Step 3: Bond distance: \[ d = 1.0\,\text{\AA} = 1.0 \times 10^{-10}\,\text{m} \]
Step 4: Calculate charge: \[ q = \frac{\mu}{d} = \frac{4.003 \times 10^{-30}}{1.0 \times 10^{-10}} = 4.003 \times 10^{-20}\,\text{C} \]
Step 5: Fraction of electronic charge: \[ \frac{q}{e} = \frac{4.003 \times 10^{-20}}{1.6 \times 10^{-19}} \approx 0.25 \] Hence, the fraction of an electronic charge on each atom is \[ \boxed{0.25} \]