Find the center of mass of the carbon monoxide molecule , given that carbon has a mass of 12 u, oxygen has a mass of 16 u , and the two atoms are 0.111 nm apart.
To find the center of mass of the carbon monoxide molecule, you need to consider the masses and positions of the carbon and oxygen atoms.
First, let's assign a coordinate system and choose a reference point. We can choose the center of mass of the carbon monoxide molecule as the origin (0,0,0).
Next, let's determine the positions of the carbon and oxygen atoms relative to the origin. Let's assume the carbon atom is located at (-0.0555 nm, 0, 0) and the oxygen atom is located at (0.0555 nm, 0, 0). The distance between the two atoms is given as 0.111 nm, so the carbon atom is half the distance to the left of the origin while the oxygen atom is half the distance to the right.
Now, let's calculate the center of mass coordinates. The center of mass is defined by the equation:
Xcm = (m1 * x1 + m2 * x2) / (m1 + m2),
Ycm = (m1 * y1 + m2 * y2) / (m1 + m2),
Zcm = (m1 * z1 + m2 * z2) / (m1 + m2),
where m1 and m2 are the masses of the carbon and oxygen atoms, respectively, and (x1, y1, z1) and (x2, y2, z2) are their respective positions.
Using these equations, we can plug in the given values:
m1 = 12 u (mass of carbon atom),
m2 = 16 u (mass of oxygen atom),
(x1, y1, z1) = (-0.0555 nm, 0, 0),
(x2, y2, z2) = (0.0555 nm, 0, 0).
Calculating each coordinate, we get:
Xcm = (12 u * -0.0555 nm + 16 u * 0.0555 nm) / (12 u + 16 u),
Ycm = (0 * 12 + 0 * 16) / (12 + 16),
Zcm = (0 * 12 + 0 * 16) / (12 + 16).
Simplifying these equations, we find:
Xcm = (0.666 nm u) / 28 u,
Ycm = 0,
Zcm = 0.
Therefore, the center of mass of the carbon monoxide molecule is located at (0.666 nm, 0, 0).