In a carbon monoxide molecule, the carbon and the oxygen atoms are separated by a distance `1.2xx10^-10m`. The distance of the centre of mass from the carbon atom is

Options

A. (a) `0.48xx10^-10m`
B. (b) `0.51xx10^-10m`
C. (c) `0.74xx10^-10m`
D. (d) `0.68xx10^-10m`

Explanation

To find the distance of the center of mass from the carbon atom in a carbon monoxide (CO) molecule, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the masses of the atoms**:
- Let the mass of the carbon atom (m_C) be 12 atomic mass units (u).
- Let the mass of the oxygen atom (m_O) be 16 atomic mass units (u).

2. **Define the distance between the atoms**:
- The distance (d) between the carbon and oxygen atoms is given as \( d = 1.2 \times 10^{-10} \) m.

3. **Set up the equation for the center of mass**:
- The center of mass (CM) of a two-particle system can be calculated using the formula:
\[ x_{CM} = \frac{m_C \cdot x_C + m_O \cdot x_O}{m_C + m_O} \]
- For our case, we can assume the carbon atom is at position 0 (x_C = 0) and the oxygen atom is at position d (x_O = d). Thus, the equation simplifies to:
\[ x_{CM} = \frac{m_C \cdot 0 + m_O \cdot d}{m_C + m_O} = \frac{m_O \cdot d}{m_C + m_O} \]

4. **Substitute the values**:
- Substitute the masses and distance into the equation:
\[ x_{CM} = \frac{16 \cdot (1.2 \times 10^{-10})}{12 + 16} \]

5. **Calculate the denominator**:
- The total mass is:
\[ 12 + 16 = 28 \]

6. **Calculate the center of mass**:
- Now substitute the values into the equation:
\[ x_{CM} = \frac{16 \cdot (1.2 \times 10^{-10})}{28} \]

7. **Perform the multiplication**:
- Calculate \( 16 \cdot (1.2 \times 10^{-10}) \):
\[ 16 \cdot 1.2 = 19.2 \]
- Thus, we have:
\[ x_{CM} = \frac{19.2 \times 10^{-10}}{28} \]

8. **Perform the division**:
- Now divide \( 19.2 \) by \( 28 \):
\[ x_{CM} \approx 0.6857 \times 10^{-10} \text{ m} \]

9. **Final answer**:
- Rounding to two decimal places, we get:
\[ x_{CM} \approx 0.68 \times 10^{-10} \text{ m} \]

### Conclusion:
The distance of the center of mass from the carbon atom is approximately \( 0.68 \times 10^{-10} \) m.