Question

The distance between a carbon atom (m = 12 u) and an oxygen atom (m = 16 u) in the CO molecule is 1.13 × 10–10 m. How far from the carbon atom is the center of mass of the molecule?

Answer 1

The distance between the center of mass of the molecule and carbon atom is 0.65 × 10⁻¹⁰ m

To answwer the question, we need to know the center of mass of CO molecule

What is the center of mass of CO molecule?

The center of mass of the CO molecule is given by

x = m₁x₁ + m₂x₂/(m₁ + m₂) where

• m₁ = mass of carbon atom = 12 u,
• x₁ = position of carbon atom = 0 m (assuming its at the origin),
• m₂ = mass of oxygen atom = 16 u and
• x₂ = position of oxygen atom = distance between molecules = 1.13 × 10⁻¹⁰ m

Substituting the values of the variables into the equation, we have

x = (m₁x₁ + m₂x₂)/(m₁ + m₂)

x = (12 u × 0 m + 16 u × 1.13 × 10⁻¹⁰ m)/(12 u  + 16 u)

x = (0 + 16 u × 1.13 × 10⁻¹⁰ m)/28 u

x = 18.08 × 10⁻¹⁰ um/28 u

x = 0.646 × 10⁻¹⁰ m

x ≅ 0.65 × 10⁻¹⁰ m

The distance between the center of mass of the molecule and carbon atom

Since the carbon atom is at x₁ = 0 m and the center of mass is at x = 0.65 × 10⁻¹⁰ m, the distance between the carbon atom and the center of mass of the molecule is d = x - x₁

= 0.65 × 10⁻¹⁰ m - 0 m

= 0.65 × 10⁻¹⁰ m

So, the distance between the center of mass of the molecule and carbon atom is 0.65 × 10⁻¹⁰ m

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