Figure P 43.18 is a model of a benzene molecule. All atoms...

Figure P 43.18 is a model of a benzene molecule. All atoms lie in a plane, and the carbon atoms $\left(m_{\mathrm{C}}=1.99 \times 10^{-26} \mathrm{kg}\right)$ form a regular hexagon, as do the hydrogen atoms $\left(m_{\mathrm{H}}=\right.1.67 \times 10^{-27} \mathrm{kg} ) .$ The carbon atoms are 0.110 nm apart center to center, and the adjacent carbon and hydrogen atoms are 0.100 nm apart center to center. (a) Calculate the moment of inertia of the molecule about an axis perpendicular to the plane of the paper through the center point $O.$ (b) Determine the allowed rotational energies about this axis.

Transcript

00:02 My dear student so we know that the moment of inertia about the x's passing through the center is equal to six times a mass of the carbon into the scale of the radius of the carbon plus six into a mass of the hydrogen atom and the square of the radius of the hydrogen carbon so we have all the values let's plug in them six into mass of a hydrogen carbon is 1 .99 multiplied by carbon is sorry 1 .99 multiplied by 10 to the power minus 26 kilograms into the radius of carbon is given there is 0 .111 nanometers 0 .110 is basically equal to 10 rest to the power minus 9 meters and whole squared plus 6 into mass of one hydrogen atom is 1 .67 multiplied by 10 raised to the power minus 27 kilograms into radius of a hydrogen atom is distance from the center to each hydrogen atom should be equal to 0 .110 plus 0 .10 right nanometers 0 .110 plus 0 .110 plus 0 .1 0 it is nano that is 10 rest of the power minus 9 and its whole square right my dear student so from here the moment of inertia equals about the axis passing through the center equals 1 .8 double 2 multiplied by 10 raise to the power minus 45 kilograms meters square right my student so this is the moment of inertia basically now the allowed energies of rotation all right so the allowed energies of rotation equals h -cutt that is plank's constant divided square divided by twice of the moment of inertia right j into j plus i right my dear student so let's simply plug in the values the value of the planks constant h -cutt that is 1 .05 multiplied by 10 raise to the power minus 34 jowls second and whole square divided by twice of moment of inertia is already being calculated by 10 rest to the power minus 45 color my dear student so j into j plus i right so from here the allowed energy rotation right energies of rotation equals 1 .84 1 .84 sorry, if we write it in the electron world, i'll do it.

03:26 I'll do a simple thing that is 0 .184 multiplied by 10 raised to the power minus 4 electron volts j into j plus i.

03:40 So here j starts from 0, 1, 2, 3, and so on...

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