In a water molecule (H2O), where is the center of mass vertically located if the oxygen atom is at y = 0?

To determine the vertical location of the center of mass of a water molecule, we need to consider the masses and positions of the constituent atoms: two hydrogen atoms and one oxygen atom. The atomic masses are approximately 16 u for oxygen and 1 u for each hydrogen atom.

Since the oxygen atom is located at a vertical position of y = 0, we can place its position in the center of our coordinate system. The two hydrogen atoms are typically found in a bent configuration around the oxygen atom, slightly above and below it. For a water molecule, the bond angle between the two hydrogen atoms is about 104.5°, and they are positioned symmetrically around the oxygen atom.

To find the center of mass, we compute the weighted average of the vertical positions of the atoms, factoring in their masses:

1. The position of the oxygen is y = 0 and its mass is 16 u.

2. The positions of the two hydrogen atoms can be approximated as y = +0.076 Å and y = -0.076 Å if we assume they are symmetrically positioned about the oxygen atom considering bond lengths in a realistic water molecule.

Now, the center of mass (y_cm) can be calculated using the