1.

Find the angular velocity of rotation of a hydrogen molecule on the first excited rotational level, if the distance between the centres of its atoms is 0.74 Å.

Answer»


Solution :The angular momentum of a rotating quantum system, including a molecule, is `L=sqrt(l(l+1))h`, where l = 0, 1, 2,
The KINETIC energy will accordingly be
`K_(rot)=L^(2)/(2J)=(l(l+1)h^(2))/(2J)`
where J is the moment of INERTIA. The kinetic energy in the first excited state is `L_(1)=hsqrt2` and the angular velocity is
`omega_(1)=L_(1)/J=(2hsqrt2)/(md^(2))`
Here d = 0.74 Å is the distance between the centres of the atoms in the molecule, and m = `1.67xx10^(-27)Kg` is the mass of HYDROGEN atom.


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