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Q 1: For particle in a box problem, answer the following questions, a) Why n=0 is...

Q 1: For particle in a box problem, answer the following questions,
a) Why n=0 is not an allowed quantum number?
b) En = 0 is not allowed for particle in a box, why?
c) Ground state wavefunction is orthogonal to the first excited state wavefunction, what
does it mean?


Q 2: An electronic system that is treated as particle in 3-D box with dimensions of 3Å x 3Å x 4Å. Calculate the wavelength corresponding to the lowest energy transition if the system has 18 electrons.


Q 3: Use the ground state wavefunction of particle-in-a-box and prove that the momentum operator is Hermitian.


Q 4: What are the differences between the conclusions for a harmonic oscillator drawn by classical mechanics and quantum mechanics?


Q 5: The fundamental frequency is 2230 cm-1 for 1H127I. If the H atom is replaced with D (isotope of H atom), calculate the fundamental frequency assuming that the force constant stays the same. Repeat the calculation if the diatomic molecule under consideration of 1H35Cl (fundamental frequency = 2886 cm-1). Explain your observations. [Do not use any other information other than what has been given in the question.]

Q 6: Given the force constant of 16O-16O bond is 1142 N.m-1, estimate the zero-point energy in the O2 bond. Explain your assumptions. What fraction of the 5.15 eV bond dissociation energy is the zero-point energy for O2?

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Answer #1

Ans1 is given below:(as The wave function for particle in a boxu given as, - 4 - 2 sin nare where 4 = wave function l = length of the box N = quaFor particle in a box, energy is given as below, En = n²h 8me² where, En = energy of electron in level na quantum state of éC) Ground state function and first excited state function are given as below,

Ground state function, (n =) Eisst excited state function (n=2) tot e infor) 2 sin ( 22 ) da 2 / (sin x) (sin 28x) dx On 4 yIt is the condition of orthogonality of two wave functions.

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