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

`6.9631* 10^(-11)\ m`

Step-by-step explanation:

I = Moment of inertia =
`4* 10^(-48)\ kg m^2`

m = Mass of two atoms = 2m =
`3.3* 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* 10^(-48)=3.3* 10^(-27)* r^2\\\Rightarrow r=\sqrt{(4* 10^(-48))/(3.3* 10^(-27))}\\\Rightarrow r=3.48155* 10^(-11)\ m`

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

`d=2r\\\Rightarrow d=2* 3.48155* 10^(-11)\\\Rightarrow d=6.9631* 10^(-11)\ m`

Therefore, the distance between the two atoms is
`6.9631* 10^(-11)\ m`