Using the particle in the 1-D box model, estimate the first 4 energy levels of the...

Using the particle in the 1-D box model, estimate the first 4 energy levels of the π-network in hexatriene, C6H8 (H2C=CH–CH=CH–CH=CH2). To calculate the box length, assume that the molecule is linear and use the values 135 and 154 pm for the C=C and C–C bonds, respectively. Only 2 out of the 6 ‘π-electrons’ of the 6 C-atoms can occupy each energy level (Pauli exclusion principle). Ignore the rest of the electrons (forming the core and the ??-bonding network). Sketch and label an energy level diagram showing the occupied levels and the first unoccupied one. What is the wavelength of the photon required to induce the HOMO-LUMO transition? Derive the expression for the photon’s wavelength symbolically! How does your numeric result compare with the experimental value of 240 nm?

Expert Solution

queen_honey_blossom answered 1 year ago

The model, particle in box can be used to estimate the energy of spectral transition in...

The model, particle in box can be used to estimate the energy of spectral transition in the molecules. (Justify the statement)

Use the particle in a box model to estimate the energies of the first electronicallyexcited states...

Use the particle in a box model to estimate the energies of the first electronicallyexcited states of ethylene, butadiene and hexatriene. Use a table of bond lengths to estimate the length of the box

Use the quantum particle wavefunctions for the kinetic energy levels in a one dimensional box to...

Use the quantum particle wavefunctions for the kinetic energy levels in a one dimensional box to qualitatively demonstrate that the classical probability distribution (any value of x is equally allowed) is obtained for particles at high temperatures.

Use the one-dimensional particle-in-a-box model with impenetrable walls and the equation R = R_0*A^(1/3) to estimate...

Use the one-dimensional particle-in-a-box model with impenetrable walls and the equation R = R_0*A^(1/3) to estimate the minimum kinetic energy of a nucleon in a nucleus. Express your answer in MeV and in terms of a number 'n' the mass number 'A', and an exponent p, which is the ratio of two integers, resulting in K = n/A^p.

Consider the one dimensional model of one-particle-in-a-box. Under what condition the two quantum levels are orthogonal....

Consider the one dimensional model of one-particle-in-a-box. Under what condition the two quantum levels are orthogonal. Namely, find the relation between m and n so that < m | n > = 0

Particle in a box is a model that is often used to look at the spectroscopy...

Particle in a box is a model that is often used to look at the spectroscopy of pi electrons in conjugated organic molecules. carotene, a precursor of retinal, a visual pigment found in the retina of the eye, has the formula given below. -carotene contains 11 conjugated double bonds which contribute 22 electrons that are delocalized along the length of the molecular chain. Each level of particle in a box has room for 2 electrons. a. The highest filled energy...

For a particle within a box it shows that the fractional difference in energy between the...

For a particle within a box it shows that the fractional difference in energy between the values adjacent is: use this formula to analyze the classic limit of the system.

What is the expectation value of kinetic energy for a particle in a box of length...

What is the expectation value of kinetic energy for a particle in a box of length ( L/2 ) in the ground eigenstate (n=1)? What about for the third excited eignestate (n=3). Explain the difference.

1. Translational motion (Particle in a box) We want to design an experiment about energy quantization...

1. Translational motion (Particle in a box) We want to design an experiment about energy quantization of a hydrogen atom via radiating a light. It is needed to predict which range of light do we have to radiate to excite an electron. Let’s assume the electron feels same potential(V=0) in certain distance(L) from the nucleus of hydrogen. 1. Let’s assume L=5.30x10-11m, me(electron mass)=9.11x10-31kg and ℏ=1.05x10-34m2 kgs-1 . (a) Make a Hamiltonian for an electron in a hydrogen atom. (b) Solve...

A) Plot the first five particle in a box wavefunctions for an electron in a 10...

A) Plot the first five particle in a box wavefunctions for an electron in a 10 Å box (starting at n = 1). Choose two of these and plot their probability density. Offer a brief interpretation. B) (10) Calculate the probability you would find the electron in the right-hand . of the box (right-hand meaning larger values of the spatial variable) if the electron were described by your fifth wavefunction (highest energy where n = 5). Calculate the probability you...

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