Find the centre of mass of the CO molecule. .Given that the atoms are `1.13 xx 10^(-10)` m apart and the ratio of the masses of the two atoms `m_(0)//m_( c) = 1.33`

Explanation

To find the center of mass of the CO molecule, we can follow these steps:

### Step 1: Understand the Problem
We have a carbon monoxide (CO) molecule consisting of a carbon atom and an oxygen atom. The distance between the two atoms is given as \(1.13 \times 10^{-10}\) m, and the ratio of their masses is given as \(\frac{m_{O}}{m_{C}} = 1.33\).

### Step 2: Define the Masses
Let:
- \(m_{C}\) = mass of the carbon atom
- \(m_{O} = 1.33 \cdot m_{C}\) (mass of the oxygen atom in terms of carbon)

### Step 3: Set Up the Coordinate System
We can place the oxygen atom at the origin of our coordinate system:
- Position of oxygen atom, \(x_{O} = 0\)
- Position of carbon atom, \(x_{C} = 1.13 \times 10^{-10}\) m

### Step 4: Use the Center of Mass Formula
The formula for the center of mass \(x_{cm}\) of a two-particle system is given by:
\[ x_{cm} = \frac{m_{O} x_{O} + m_{C} x_{C}}{m_{O} + m_{C}} \]

### Step 5: Substitute the Values
Substituting the known values into the formula:
\[ x_{cm} = \frac{(1.33 \cdot m_{C}) \cdot 0 + m_{C} \cdot (1.13 \times 10^{-10})}{1.33 \cdot m_{C} + m_{C}} \]
This simplifies to:
\[ x_{cm} = \frac{m_{C} \cdot (1.13 \times 10^{-10})}{(1.33 + 1) \cdot m_{C}} = \frac{1.13 \times 10^{-10}}{2.33} \]

### Step 6: Calculate the Center of Mass
Now, we can calculate \(x_{cm}\):
\[ x_{cm} = \frac{1.13 \times 10^{-10}}{2.33} \approx 0.485 \times 10^{-10} \text{ m} \]

### Step 7: Interpret the Result
The center of mass is located at approximately \(0.485 \times 10^{-10}\) m from the oxygen atom.

### Final Answer
The center of mass of the CO molecule is approximately \(0.485 \times 10^{-10}\) m from the oxygen atom.

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