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.

=7.28 x 10^-46 kg*m^2
=13.74 x 10^-10m

Is this correct?

To estimate the effective distance between the oxygen atoms, we need to use the moment of inertia and the total mass of the molecule.

The moment of inertia (I) of a molecule is related to the effective distance (r) between the atoms by the formula:

I = μr^2

where μ is the reduced mass given by:

μ = (m1 * m2) / (m1 + m2)

In this case, the total mass of the molecule is given as 5.3 x 10^-26 kg. Since the molecule consists of two oxygen atoms with the same mass, each oxygen atom has a mass of (5.3 x 10^-26 kg) / 2.

Now let's calculate the reduced mass (μ):

μ = (5.3 x 10^-26 kg / 2) * (5.3 x 10^-26 kg / 2) / (5.3 x 10^-26 kg / 2 + 5.3 x 10^-26 kg / 2)

Simplifying,

μ = (5.3 x 10^-26 kg / 2) * (5.3 x 10^-26 kg / 2) / (5.3 x 10^-26 kg)

μ = (5.3 x 10^-26 kg / 2) / (5.3 x 10^-26 kg)

μ = 1 / 2

So, the reduced mass is 1/2 times the mass of one oxygen atom.

Now we can use the given moment of inertia (1.9 x 10^-46 kg*m^2) and the calculated reduced mass to determine the effective distance (r).

1.9 x 10^-46 kg*m^2 = (1/2) * (5.3 x 10^-26 kg) * r^2

Simplifying,

r^2 = (1.9 x 10^-46 kg*m^2) / [(1/2) * (5.3 x 10^-26 kg)]

r^2 = 2 * (1.9 x 10^-46 kg*m^2) / (5.3 x 10^-26 kg)

r^2 = 0.716 x 10^-20 m^2

Taking the square root of both sides,

r = √(0.716 x 10^-20 m^2)
r = 0.846 x 10^-10 m

So, the estimated effective distance between the oxygen atoms is approximately 0.846 x 10^-10 m, or 8.46 x 10^-11 m.

Therefore, the answer 13.74 x 10^-10 m is not correct.