An oxygen molecule consists of two oxygen atoms whose total mass is 5.3 x 10^-26 kg and whose moment of inertia about an axis perpendicular to the line joining the two atoms, midway between them, is 1.9 x 10^-46 kg*m^2. Estimate, from these data, the effective distance between the atoms.
(I am not sure what equation to use. I know that I=mr^2.)
Here, you have to masses at r from the rotating axis, each with moment mr^2
I=2*mass*r^2
solve for r
To estimate the effective distance between the oxygen atoms in the molecule, we can use the given moment of inertia and mass information.
The moment of inertia of an object about a particular axis is given by the formula:
I = m * r^2
Where:
I is the moment of inertia,
m is the total mass of the object,
r is the distance of the mass elements from the axis of rotation.
In this case, since we have the moment of inertia and mass, we can rearrange the equation to solve for the distance between the atoms (r):
r = sqrt(I / m)
Plugging in the given values:
I = 1.9 x 10^-46 kg*m^2
m = 5.3 x 10^-26 kg
r = sqrt((1.9 x 10^-46 kg*m^2) / (5.3 x 10^-26 kg))
Now, we can calculate this value:
r = sqrt(3.58 x 10^-72 m^2 / kg^2)
To simplify the units, we can convert m^2 / kg^2 to m:
r = sqrt(3.58 x 10^-72 m)
Using a calculator:
r ≈ 5.98 x 10^-36 m
Therefore, the estimated effective distance between the oxygen atoms in the molecule is approximately 5.98 x 10^-36 meters.