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. `0.48xx10^-10m`
B. `0.51xx10^-10m`
C. `0.74xx10^-10m`
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 use the formula for the center of mass (CM) of a two-particle system. The formula is given by:

\[ x_{CM} = \frac{m_1 x_1 + m_2 x_2}{m_1 + m_2} \]

Where:
- \( m_1 \) is the mass of the carbon atom.
- \( m_2 \) is the mass of the oxygen atom.
- \( x_1 \) is the position of the carbon atom (we can take this as 0).
- \( x_2 \) is the position of the oxygen atom (which is the distance between the two atoms).

### Step 1: Identify the masses
- The atomic mass of carbon (\( m_1 \)) is 12 u (atomic mass units).
- The atomic mass of oxygen (\( m_2 \)) is 16 u.

### Step 2: Define the positions
- Let the position of the carbon atom be \( x_1 = 0 \) m.
- The position of the oxygen atom will be \( x_2 = 1.2 \times 10^{-10} \) m (the distance between the two atoms).

### Step 3: Substitute values into the center of mass formula
Using the center of mass formula:
\[ x_{CM} = \frac{m_1 x_1 + m_2 x_2}{m_1 + m_2} \]

Substituting the values:
\[ x_{CM} = \frac{(12 \, \text{u}) \cdot (0) + (16 \, \text{u}) \cdot (1.2 \times 10^{-10} \, \text{m})}{12 \, \text{u} + 16 \, \text{u}} \]

This simplifies to:
\[ x_{CM} = \frac{0 + 19.2 \times 10^{-10} \, \text{u m}}{28 \, \text{u}} \]

### Step 4: Calculate the center of mass
\[ x_{CM} = \frac{19.2 \times 10^{-10}}{28} \]

Calculating this gives:
\[ x_{CM} = 0.6857142857 \times 10^{-10} \, \text{m} \approx 0.688 \times 10^{-10} \, \text{m} \]

### Step 5: Final answer
Thus, the distance of the center of mass from the carbon atom is approximately:
\[ x_{CM} \approx 0.688 \times 10^{-10} \, \text{m} \]