The particle in a one-dimensional box can be used as a crude model for conjugated systems-hydrocarbons with alternating double and single bonds-such as 1,3,5,7- octatetraene. _CH CH CH CH CH CH CH₂ CH₂ Assume a C-C bond length of 156 pm and a C=C bond length of 138 pm. Since there are eight electrons, they go in pairs in the first four energy levels, n = 1, 2, 3, 4. Part A Compute the energy of light required to excite an n = 4 electron to the n = 5 state. Express your answer in joules to three significant figures. 17| ΑΣΦ E = Submit Review | Constants | Periodic Table Request Answer ?

The particle in a one-dimensional box can be used as a crude model for conjugated systems-hydrocarbons with alternating double and single bonds-such as 1,3,5,7- octatetraene. _CH CH CH CH CH CH CH₂ CH₂ Assume a C-C bond length of 156 pm and a C=C bond length of 138 pm. Since there are eight electrons, they go in pairs in the first four energy levels, n = 1, 2, 3, 4. Part A Compute the energy of light required to excite an n = 4 electron to the n = 5 state. Express your answer in joules to three significant figures. 17| ΑΣΦ E = Submit Review | Constants | Periodic Table Request Answer ?

Principles of Modern Chemistry

8th Edition

ISBN:9781305079113

Author:David W. Oxtoby, H. Pat Gillis, Laurie J. Butler

Publisher:David W. Oxtoby, H. Pat Gillis, Laurie J. Butler

Chapter4: Introduction To Quantum Mechanics

Section: Chapter Questions

Problem 39P: Chapter 3 introduced the concept of a double bond between carbon atoms, represented by C=C , with a...

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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.
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.
Prove that the potential energy of the electron is Etotal -e?/ (8πεoΥ)
The ground state of H, has the electron configuration (og1s)². There are excited states that have the following configurations (a) (ơg1s)"(ơins)" (b) (Tg1s)(ơiis)²
Three of the term symbols that correspond to a nd3 electron configuration are 2P, 2F, and 4P. Rank these in terms of increasing energy.
Identify the ground term from each set of terms: (a) ¹p, ³p,³F,¹G; (b) ³P,5D,³H,¹1,¹G; (c) 6S,4P,4G,²1.
Write the term symbols for the 5f12 electron configuration. Show all work.
6. The particle on a ring is a useful model for the motion of electrons around the coronene ring. See a 2-D representation of the coronene molecule below; the dashed line around the periphery of the molecule indicates the electron path. We may treat the structure as a circular ring of radius 420 pm, with 14 electrons in the conjugated system moving along the perimeter of the ring. Assuming that, in the ground state of the molecule, each state is occupied by two electrons, (a) calculate the energy and angular momentum of an electron in the highest occupied level, and (b) calculate the frequency of radiation that can induce a transition between the highest occupied and lowest unoccupied levels.
Write the valence bond wavefunction for the one cr andtwo n bonds in a nitrogen molecule, N2 .
5. (a) Use the hydrogen-like model z2 (in eV) En --13.6 to calculate the total energy of the three electrons of lithium (Li), which has the electron configuration: 1s? 2s'. The three ionization energies for Li(g) are: IE, = 5.392 ev; IE2 = 75.64 eV; IE = 122.5 ev. With the help of Koopman's theorem, what is the total energy of ropulsion between lithium's three electrons (in kJ mol')?
Evaluate the energy for two MO's generated by combining an H 1s atomic orbital with a F 2p atomic orbital. Use the equation: 1 2–252[H, 1 [H+H»- 2SH2]± 2-2s? + 4H, + H, -4SH„H„ -2H(H, +2SH, – 28²H,)| Carry out the calculation for S = 0.1, 0.2, and 0.6 to mimic the effect of decreasing the atomic separation in the molecule. Use the parameters: H,,= -13.6 ev, H22 = -18.6 eV, and H,2 = -1.75S H11H22 .
4G I 5:53 2.30 O Yo 40 52% KB/s 1. The C-C stretch in allene (H,C-C=CH,) is about 1650 cm'; the C-H stretch is about 3,100 cm". Calculate the corresponding wavelengths (in nm) and energies (in kJ/mol) of these vibrations. () II