Question

An oxygen molecule consists of two oxygen atoms, (O2), whose total mass is 5.3 × 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 × 10–46 kg • m2 . From these data, estimate the effective distance d between the atoms?

Answer 1

Answer : The distance between the two atoms is $1.2\times 10^{-10}m$

Explanation :

The The formula used for moment of inertia for one atom is:

$I=(\frac{m}{2})r^2$

The formula used for moment of inertia for two atom is:

$I=2(\frac{m}{2})r^2$

where,

I = moment inertia = $1.9\times 10^{-46}kg.m^2$

r = distance of atom from axis of rotation

m = mass of atom = $5.3\times 10^{-26}kg$

Now put all the given values in the above formula, we get:

$I=2(\frac{m}{2})r^2$

$1.9\times 10^{-46}kg.m^2=2(\frac{5.3\times 10^{-26}kg}{2})r^2$

$r=6.0\times 10^{-11}m$

Now we have to calculate the distance between the two atoms.

Formula used :

$d=2r$

where,

d = distance between the two atoms

$d=2\times 6.0\times 10^{-11}m=1.2\times 10^{-10}m$

Therefore, the distance between the two atoms is $1.2\times 10^{-10}m$