Question

The separation between C and O-atoms in CO is 1.2 \AA. The distance of carbon atom from the centre of mass is

• A. 0.3 \AA
• B. 0.7 \AA
• C. 0.5 \AA
• D. 0.9 \AA

Hint:

Centre of mass is closer to heavier atom (oxygen).

Answer 1

The Correct Option is B

To solve this problem, we need to calculate the distance of the carbon atom from the center of mass of the carbon monoxide (CO) molecule.

The separation between the carbon and oxygen atoms in CO is given as \(1.2 \, \text{\AA}\). This is the total distance between the C and O atoms.

The center of mass (\(COM\)) of a system is calculated using the formula:

\(COM = \frac{m_1 x_1 + m_2 x_2}{m_1 + m_2}\)

Where:

• \(m_1\) and \(m_2\) are the masses of the carbon and oxygen atoms, respectively.
• \(x_1\) and \(x_2\) are their respective positions from a reference point (usually one of the atoms).

Let us take the carbon atom as the origin (\(x_1 = 0\)), then \(x_2 = 1.2 \, \text{\AA}\). We need to find the position of the center of mass relative to carbon, i.e., \(x = \frac{m_2 \cdot 1.2}{m_1 + m_2}\).

Using the atomic masses typically found on a periodic table, we know:

• Molecular weight of Carbon (\(C\)) = 12 u
• Molecular weight of Oxygen (\(O\)) = 16 u

Substitute these values into the formula:

\(COM = \frac{16 \cdot 1.2}{12 + 16}\)

Performing the calculation:

• \(= \frac{19.2}{28}\)
• \(\approx 0.6857 \, \text{\AA}\)

Approximating to one decimal place: \(0.7 \, \text{\AA}\)

Therefore, the distance of the carbon atom from the center of mass is approximately \(0.7 \, \text{\AA}\). This matches the given correct option.