Question

An hydrogen molecule consists of two hydrogen atoms whose total mass is 3.3×10−27 kg and whose moment of inertia about an axis perpendicular to the line joining the two atoms, midway between them, is 4.0×10−48 kg⋅m2 . Part A From these data, estimate the effective distance between the atoms.

Answer 1

Answer:

$6.9631\times 10^{-11}\ m$

Explanation:

I = Moment of inertia = $4\times 10^{-48}\ kg m^2$

m = Mass of two atoms = 2m = $3.3\times 10^{-27}\ kg$

r  = distance between axis and rotation mass

Moment of inertia of the system is given by

$I=mr^2\\\Rightarrow I=2mr^2\\\Rightarrow 4\times 10^{-48}=3.3\times 10^{-27}\times r^2\\\Rightarrow r=\sqrt{\frac{4\times 10^{-48}}{3.3\times 10^{-27}}}\\\Rightarrow r=3.48155\times 10^{-11}\ m$

The distance between the atoms will be two times the distance between axis and rotation mass.

$d=2r\\\Rightarrow d=2\times 3.48155\times 10^{-11}\\\Rightarrow d=6.9631\times 10^{-11}\ m$

Therefore, the distance between the two atoms is $6.9631\times 10^{-11}\ m$