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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.Schrodinger and de Broglie suggested a ‘Wave—particle duality" for small particles—that is, if electromagnetic radiation showed some particle-like properties, then perhaps small punicles might exhibit same wave-like properties. Explain. How does the wave mechanical picture of the atom fundamentally differ from the Bohr model? How do wave mechanical arbitals differ from Bohr’s orbits? What does it mean to say that an orbital represents a probability map for an electron?Using a simple particle-in-a-box model for the multiple bonding in 1,2-butadiene (see Example 4.7) and the n=2 wave function for the weakest bound electron, calculate the probability of finding the electron in an 0.1 interval centered midway between the two inner carbon atoms (that is, the center is at x=2.11 , so this interval is from x1=2.06 to x2=2.16 ). Then calculate the probability of finding the electron in an 0.1 interval centered midway between an end carbon atom and the carbon atom that is double-bonded to it in the Lewis dot structure. (You may calculate the appropriate integrals or estimate the relevant areas under the curve graphically.) Then recalculate the probabilities by approximating the integral as |( x 0)|2x , where x0 is evaluated in the middle of the range from x1 to x2 . Finally, explain why you can’t approximate the integral needed for Problem 37(a) in this way.
- Consider Figure 11.4 and choose the correct phrase: As the vibrational quantum number increases, the extension of the vibration increases/decreases/stays the same while the average length of the oscillator itself increases/decreases/stays the same. Explain your choices.Explain why cyclopentadiene easily accepts an electron to become cyclopentadienyl anion C5H5, which is abbreviated Cp in organic or organometallic chemistry.Why does the wavefunction 4,4,0 not exist? Similarly, why does a 3f subshell not exist? See exercise 11.73 for notation definition.
- 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.Explores the vibrational and rotational energy levels of the hydrogen halides. Experimental data are given below. Hydrogen halides kf (kg/s?) R (pm) HF 970.0 91.7 HCI 480.0 127.5 HBr 410.0 141.4 HI 320.0 160.9 For one mole of each HF, determine the following quantities. AE10 = Incorrect b. The number of vibrational energy levels occupied at 300K levels 3 Incorrect c. The spacing between the two lowest rotational energy levelsA). A molecule can have various types of energies (translational, rotational, vibrational, and electronic), the sum of which is the molecule's total energy. ?trans=(?^2?+?^2?+?^2?)(ℎ^2/8??^2/3) ?rot=?(?+1)ℎ^2/8?2? ?vib=(?+1/2)(ℎ?) In the equations, ??, ??, ??, ?, and ? are quantum numbers, ℎ is Planck's constant, ? is the mass of the molecule, ? is the volume of the container, ? is the moment of inertia of the molecule, and ? is the fundamental vibration frequency. For carbon monoxide, CO , the moment of inertia is ?=1.45×10−46 kg⋅m2, and the fundamental vibration frequency is ?=2130 cm−1. Let ?=12.8, and let all the quantum numbers be equal to 11 . Calculate the translational, rotational, and vibrational energies per mole of CO for these conditions. ?trans= J/mol ?rot= J/mol ?vib= J/mol B). If the electronic energy of CO is 9.14 eV per molecule, calculate the total energy of CO per mole. ?total= J/mol C). Which types of energy are…
- physical chemistry 4. Sketch the shape of the ground state wavefunction for a harmonic oscillator, and the wavefunction for the next highest energy. Be sure to include the potential energy curve on the graph. What are the corresponding vibrational quantum numbers and the energies in terms of v, the classical vibrational frequency? a. A diatomic molecule with a reduced mass of 5.00 amu has a force constant of 1000 N m¹. What is the vibrational frequency in cm¹?8. Electronic Spectroscopy. Vibrational spectroscopy refers to changes in vibrational energy levels. Electronic spectroscopy refers to the photon energy absorbed or emitted by a molecule from electron transitions between different possible electronic states. On the diagram below, Draw arrows to illustrate the processes, and Label with the letters shown in bold. a) Franck-Condon principle for electronic excitation (F-C), from vibrational ground state v = 0. b) Collisional Relaxation in the excited states without photon emission (CR) c) Return to the ground state via Fluorescence (F) d) Intersystem Crossing (ISC) e) Return to the ground state via Phosphorescence (P) f) Infra Red absorbance of one quantum of vibrational energy from v = 0 in the ground state (IR) Raman scattering that allows transition from v = 0 to v = 1, in the ground state (RAMAN) On the x-axis, indicate the bond lengths re and ro for the ground electronic state only. Draw an arrow to show the magnitude of the Zero…A possible excited state for the helium atom has the configuration 1s'2p1 1. Find the S-L-J term symbols for this electronic configuration. ( Hint: there are 12 microstates). Which term is the lowest in energy?