The distance between the centres of carbon and oxygen atoms in the carbon monoxide molecule is `1.130Å` . Locate the centre of mass of the molecule relative to the carbon atom .

Options

A. `5.428Å`
B. `1.130Å`
C. `0.6457Å`
D. `0.3260Å`

Answer

To locate the center of mass of the carbon monoxide (CO) molecule relative to the carbon atom, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Given Data:**
- Distance between the centers of carbon and oxygen atoms, \( d = 1.130 \, \text{Å} = 1.130 \times 10^{-10} \, \text{m} \)
- Atomic mass of carbon (C) = 12 u
- Atomic mass of oxygen (O) = 16 u

2. **Calculate the Total Mass of the CO Molecule:**
\[ \text{Total mass} = \text{Mass of Carbon} + \text{Mass of Oxygen} = 12 \, \text{u} + 16 \, \text{u} = 28 \, \text{u} \]

3. **Use the Center of Mass Formula:**
The position of the center of mass (CM) relative to the carbon atom can be calculated using the formula:
\[ x_{CM} = \frac{m_O \cdot d}{m_C + m_O} \]
where:
- \( m_O \) = mass of oxygen = 16 u
- \( m_C \) = mass of carbon = 12 u
- \( d \) = distance between the two atoms = \( 1.130 \times 10^{-10} \, \text{m} \)

4. **Substituting the Values:**
\[ x_{CM} = \frac{16 \, \text{u} \cdot (1.130 \times 10^{-10} \, \text{m})}{28 \, \text{u}} \]

5. **Calculating the Center of Mass:**
\[ x_{CM} = \frac{18.08 \times 10^{-10} \, \text{m}}{28} \approx 0.6457 \times 10^{-10} \, \text{m} \]

6. **Convert to Ångstroms:**
Since \( 1 \, \text{Å} = 10^{-10} \, \text{m} \),
\[ x_{CM} \approx 0.6457 \, \text{Å} \]

### Final Answer:
The center of mass of the carbon monoxide molecule relative to the carbon atom is approximately \( 0.6457 \, \text{Å} \).

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