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- Chapter 3 introduced the concept of a double bond between carbon atoms, represented by C=C , with a length near 1.34 Å. The motion of an electron in such a bond can be treated crudely as motion in a one-dimensional box. Calculate the energy of an electron in each of its three lowest allowed states if it is confined to move in a one-dimensional box of length 1.34 Å. Calculate the wavelength of light necessary to excite the electron from its ground state to the first excited state.22) HO. + H,C=c=0Calculate the expectation values of potential and kinetic energies for the 1s state of of a hydrogenlike atom. 3/2 e-Zr/ao Ze? R10(r) = 2 ao 4TtEgr
- 1. The oxygen 1s electron in the compound TIO2 has a binding energy of 530.0 eV relative to the Fermi energy of the solid. Using a Al Ka source (photon energy of 1486.6 eV), what is the kinetic energy of the photoelectrons ejected from the oxygen 1s level as measured by an electron analyzer with work function equal to 5.0 eV? Please show your work.The vibrational frequency of the hydrogen chloride HCl diatomic molecule is 8.97 x 1013Hz. chloride atom is 35.5 times more massive than hydrogen atom. (mµ = 1.67 x 0-27kg,c = 3.0 x 10°m/s) a) What is the force constant of the molecular bond between the hydrogen and the chloride atoms? b) What is the energy of the emitted photon when this molecule makes a transition between adjacent vibrational energy levels? c) What is the wavelength of the emitted photon? d) The possible wavelengths of photons emitted with the HCl molecule decays from the 2nd excited state eventually to the ground state(0 state).3. Which process is expected to involve the highest energy? Transition from n=5 to n=1 in hydrogen atom Vibrational bending mode of CO2 at 526 cm C) Transition from n=4 to n33 in hydrogen atom D) H2O molecules excited by microwave radiation E) Rotation of H2O molecules
- β-Carotene (1) is a linear polyene in which 10 sing le and 11 double bonds alternate along a chain of 22 carbon atoms. If the length of each CC bond is taken to be about 140 pm , then the length L of the molecular box in β-carotene is L = 2.94 nm. Estimate the wavelength of the light absorbed bythis molecule when it undergoes a t rans it ion from its ground state to the next higher excited state.A typical plasma in an ICP increases the temperature of an atom by about 9000 K (i.e. from 273 K to 9273 K). If the energy difference for an atom between its ground and excited state is ΔE = 3.00 * 10-19 J, calculate the ratio of electrons in the excited state compared to the ground state. Assume the degeneracy of the ground state is 1, while the excited state is 3. constant: kboltzman = 1.381 * 10-23 J/K12 J (er? nu? nu? ng2 ng (2p)] configuration is for 02 A O +o, 2 co
- 4. The n-electron system in benzene may be approximated as a particle-on-a-ring with a radius of r, which is also the length of the C-C bonds in the ring. This bond length is approximately 1.39 Å. The energy levels for the p-o-a-r are given by: n'h E, = where n = 0, ±1, ±2, ±3, .. 2m r The six t-electrons in benzene fill the (singly degenerate) n30 level, and the (doubly degenerate) n=±1 level. The first excited state, then corresponds to exciting an electron from n=1 to n=2. a) Using the given bond length, calculate the energy change for the benzene molecule as an electron is excited from n=1 to n=2. b) Calculate the wavelength of light that benzene would need to absorb to undergo that energy change. Compare that with the experimental value of 268 nm. c) In what portion of the electromagnetic spectrum is this wavelength? d) Using the experimental wavelength from part b above, calculate the effective bond length in benzene. e) Is the particle-on-a-ring approximation valid? Give a…4. The n-electron system in benzene may be approximated as a particle-on-a-ring with a radius of r, which is also the length of the C-C bonds in the ring. This bond length is approximately 1.39 A. The energy levels for the p-o-a-r are given by: n'h E, ,where n = 0, t1, ±2, 13, . 2m,r? The six r-electrons in benzene fill the (singly degenerate) n 0 level, and the (doubly degenerate) n=t1 level. The first excited state, then corresponds to exciting an electron from n=1 to n=2. a) Using the given bond length, calculate the energy change for the benzene molecule as an electron is excited from n=1 to n=2. b) Calculate the wavelength of light that benzene would need to absorb to undergo that energy change. Compare that with the experimental value of 268 nm. c) In what portion of the electromagnetic spectrum is this wavelength? d) Using the experimental wavelength from part b above, calculate the effective bond length in benzene. e) Is the particle-on-a-ring approximation valid? Give a…INe]3s 3p is a electronic configuration of Select ane: O Aluminum Silicon magnesium Sodium