mp-Chapt-8-sol - Inha University Department of Physics 1...

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Unformatted text preview: Inha University Department of Physics 1. The energy needed to detach the electron from a hydrogen atom is 13.6 eV, but the energy needed to detach an electron from a hydrogen molecule is 15.7 eV. Why do you think the latter energy is greater? sol The nuclear charge of +2 e is concentrated at the nucleus, while the electron charges' densities are spread out in (presumably) the 1 s subshell. This means that the additional attractive force of the two protons exceeds the mutual repulsion of the electrons to increase the binding energy. 3. At what temperature would the average kinetic energy of the molecules in a hydrogen sample be equal to their binding energy? sol Using 4.5 eV for the binding energy of hydrogen, Chapter 8 Problem Solutions K 10 5 3 eV/K 10 8.62 eV 5 4 3 2 or eV 5 4 2 3 4 5- × = × = = . . . T kT Inha University Department of Physics 5. When a molecule rotates, inertia causes its bonds to stretch. (This is why the earth bulges at the equator.) What effects does this stretching have on the rotational spectrum of the molecule? sol The increase in bond lengths in the molecule increases its moment of inertia and accordingly decreases the frequencies in its rotational spectrum (see Equation (8.9)). In addition, the higher the quantum number J (and hence the greater the angular momentum), the faster the rotation and the greater the distortion, so the spectral lines are no longer evenly spaced. Quantitatively, the parameter I (the moment of inertia of the molecule) is a function of J , with I larger for higher J . Thus, all of the levels as given by Equation (8.11) are different, so that the spectral lines are not evenly spaced. (It should be noted that if I depends on J , the algebraic steps that lead to Equation (8.11) will not be valid.) 7. The J =0 & J =1 rotational absorption line occurs at 1.153x10 11 Hz in 12 C 16 O and at 1.102x10 11 Hz in ?...
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This note was uploaded on 11/29/2010 for the course PHY 111 taught by Professor Kim during the Spring '10 term at 카이스트, 한국과학기술원.

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mp-Chapt-8-sol - Inha University Department of Physics 1...

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