In a carbon monoxide molecule, the carbon and the oxygen atoms are separted by a distance ` 1.12 xx 10^(-10)` m. The distance of the centre of mass from the carbon atom is

A. ` 0.64 xx 10^(-10)m`
B. `0.56xx10^(-6) `m
C. `0.51 xx 10^(-10) m`
D. `0.48 xx 10^(-10)` m

Options

A. ` 0.64 xx 10^(-10)m`
B. `0.56xx10^(-6) `m
C. `0.51 xx 10^(-10) m`
D. `0.48 xx 10^(-10)` m

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 1: Define the variables
Let:
- \( m_1 \) = mass of carbon atom = 12 u (atomic mass units)
- \( m_2 \) = mass of oxygen atom = 16 u
- \( d \) = distance between carbon and oxygen = \( 1.12 \times 10^{-10} \) m
- \( x \) = distance from the carbon atom to the center of mass
- \( d - x \) = distance from the oxygen atom to the center of mass

### Step 2: Write the equation for center of mass
The equation for the center of mass (CM) is given by:
\[ m_1 \cdot x = m_2 \cdot (d - x) \]

### Step 3: Substitute the known values
Substituting the known masses into the equation:
\[ 12 \cdot x = 16 \cdot (1.12 \times 10^{-10} - x) \]

### Step 4: Expand and rearrange the equation
Expanding the right side:
\[ 12x = 16 \cdot 1.12 \times 10^{-10} - 16x \]
Rearranging gives:
\[ 12x + 16x = 16 \cdot 1.12 \times 10^{-10} \]
\[ 28x = 16 \cdot 1.12 \times 10^{-10} \]

### Step 5: Solve for \( x \)
Now, divide both sides by 28:
\[ x = \frac{16 \cdot 1.12 \times 10^{-10}}{28} \]

### Step 6: Simplify the expression
Calculating the right side:
\[ x = \frac{16 \cdot 1.12}{28} \times 10^{-10} \]
\[ x = \frac{17.92}{28} \times 10^{-10} \]
\[ x = 0.64 \times 10^{-10} \, \text{m} \]

### Final Answer
Thus, the distance of the center of mass from the carbon atom is:
\[ \boxed{0.64 \times 10^{-10} \, \text{m}} \]