Assume that the states of the π electrons of a conjugated molecule can be approximated by the wavefunctions of a particle in a one-dimensional box, and that the magnitude of the dipole moment can be related to the displacement along this length by μ = −ex. Show that the transition probability for the transition n = 1 → n = 2 is non-zero, whereas that for n = 1 → n = 3 is zero. Hints: The following relation will be useful: sin x sin y = 1/2cos(x − y) − 1/2cos(x + y). Relevant integrals are given in the Resource section.

Q: (structure below) is proposed as a model compound for an application of the particle-in-a-ring…

A:

Q: P11B.7 The microwave spectrum of 16O*CS gave absorption lines (in GHz) as follows: 1 3 4 325…

A:

Q: Calculate the separation between the two lowest energy levels for an N2 molecule in a one-…

A:

Q: A particle freely moving in one dimension x with 0 ≤ x ≤ ∞ is in a state described by the normalized…

A: Given normalized wave function ψ(x) = a1/2e–ax/2 where 'a' is a constant. Particle freely moving in…

Q: For the system described in Exercise E7B.1(a) (A possible wavefunction for an electron in a region…

A: Here in question exercise is not mentioned, so here assume particle in 1-D box system. When mod…

Q: The moment of inertia of an SF6 molecule is 3.07 × 10−45 kg m2. What is the minimum energy needed to…

A: Given:   The moment of interia of an SF6 molecule is 3.07×10-45 kg m2.

Q: The rotation motion of HCl molecules can be analyzed by treating each molecule as a rigid rotational…

A: Given:  rigid rotational constant B= 2.07x10-22 Joules. To Calculate: a) The frequency of radiation…

Q: 8.11a Confirm that the operator i = (h/i)d/dø, where ø is an angle, is hermitian.

A:

Q: The ground-state wavefunction for a particle confined to a one dimensional box of length L is Ψ…

A: Ans.

Q: The wavefunction of one of the d orbitals is proportional to sin2θ sin 2ϕ. At what angles does it…

A:

Q: A normalized wavefunction for a particle confined between 0 and L in the x direction is ψ = (2/L)1/2…

A: A normalized wavefunction for a particle confined between 0 and L in the x direction is ψ = (2/L)1/2…

Q: Calculate the energy of the quantum involved in the excitation of (i) an electronic oscillation of…

A: We will use the formula E=hv, where “h” and “v” are plancks constant and frequency respectively.

Q: 3. What is the wavenumber of an electromagnetic radiation of frequency 4.3 x 104 Hz?

A: Given data  Frequency (v) = 4.3 × 1014 Hz We know, 1Hz = s-1 Therefore, frequency (v) = 4.3 × 1014…

Q: Consider a particle in the following 1D box. The potential in this box has the form: 1 2. V = kx² 2…

A:

Q: 7A.3(b) Calculate the speed to which a stationary 'He atom (nmass 4.0026m.,) would be accelerated if…

A: Dear Student, Since the question you have asked involves multiple sub questions. According to our…

Q: (iii) Show that the wave function of the particle in the potential well is NA X w.(x) = C sin n =…

A:

Q: Functions of the form sin(nπx/L), where n = 1, 2, 3 …, are wavefunctions in a region of length L…

A: The wavefunction is given as,ψ = sin nπxLFor n=1,     ψ1 = sin πxLFor n=2,     ψ1 = sin 2πxL

Q: Calculate the value of ml for a proton constrained to rotate in a circle of radius 100 pm around a…

A: Given, Radius of the circle = 100 pm =…

Q: A possible wavefunction for an electron in a region of length L (i.e. from x=0 to x=L) is 2 πχ. sin…

A:

Q: ħ² The quantized energies of the rigid rotor are given by E, = 1/-/J (J -J(J + 1). If J = 2, what…

A: Rigid rotor is a mechanical model of rotating systems. Rigid rotor is a three dimensional rigid…

Q: For the same system as in Exercise E7C.3(a) (Functions of the form sin(nπx/L), where n = 1, 2, 3 …,…

A:

Q: A rotating diatomic molecule absorbs radiation and has moment of inertia, I, equal to 1.00 x 10-46…

A:

Q: If a nitrogen molecule is trapped in a hypothetical 1-D box of length 1.10 cm, at what value of the…

A: Translational energy :-            It is the energy which is associated with displacement of a…

Q: Determine which of the following transitions are allowed. 'P: E IS. P, E 'S. 'D2 E 'S, 'D2 E 'P2 3D.…

A: The transition that are allowed is given below

Q: A diatomic molecule is modeled as a Morse oscillator, and one finds that its energy level…

A:

Q: What are the atomic term symbols for an electronic configuration of s2p?

A: Electronic configuration of an atom describes the arrangement of electrons in orbitals of an atom.

Q: The particle on a ring is a useful model for the motion of electrons around the porphine ring, the…

A:

Q: (structure below) is proposed as a model compound for an application of the particle-in-a-ring…

A:

Q: Calculate the wavelength of a photon needed to excite a transition between neighbouring energy…

A:

Q: 421) The moment of inertia of an SF, molecule is 3.07 x 10 kg m. What is the minimum energy needed…

A: Given, the moment of inertia of an SF6 molecule = 3.07×10-45 kg m2 The minimum energy needed to…

Q: Determine the energetic difference between state n = 2 and n = 1 for a proton in a one-dimensional…

A:

Q: For a particle in a two-dimensional square box of length L, if the particle is in the state w2,3 (x,…

A: Wavefunction of a particle in 2D is given by

Q: (structure below) is proposed as a model compound for an application of the particle-in-a-ring…

A:

Q: The spacing of lines in the microwave spectrum of 27Al1H is 12.604 cm−1; calculate the moment of…

A: The spacing between two lines in a microwave spectrum of a diatomic molecule is equal to 2B, where B…

Q: The energy required for the excitation from the 2nd to the 3rd excited levels in a particle moving…

A:

Q: If an electron confined to a potential well of width 1.40 nm with infinite barriers on both sides…

A: Given data:

Q: The C-H bond in ethanol vibrates at a frequency of 3000 cm ¹. What frequency (s 1) of light is…

A: Light is required to change the vibrational quantum from v=0 to v=1,  that has same energy as the…

Q: (structure below) is proposed as a model compound for an application of the particle-in-a-ring…

A: This is the problem of MO diagram of a octatetraene in 2 d box.

Q: 7A.1(b) Calculate the size of the quantum involved in the excitation of (i) an electronic…

A:

Q: The microwave spectrum of a diatomic molecule (reduced mass 1.66 x 10" kg) consists of a series of :…

A: Microwave Spectroscopy - The microwave spectrum usually ranges from 1GHz to 100GHz.  Reduced mass =…

Q: Confirm that the wavefunction Y(x,t)= e(px-Et)/h is a solution of the one-dimensional time- 2.…

A:

Q: Calculate the wavelength of the photon needed to excite a transition between neighbouring energy…

A: The wavelength of harmonic oscillator is given by,

Q: P7E.6 Before attempting these calculations, see Problem P7E.5. The following data give the…

A: The force constant k is related to wavenumber ν- by using the formula  ν-=12πckμ c is the speed of…

Q: A measurement of the vibrational energy levels of 12cl°0 applying Morse potential gives the…

A: Given, Morse potential relationship: ν(n) = 2170.21n+12cm-1 - 13.461n+122cm-1 n is vibrational…

Q: A hydrogen atom rotates in three dimensions at a fixed distance of 100 pm from a fixed point. Ca…

A: The energy of particle with quantum number that is given is calculated using the formula, E=J22mr2…

Q: Which of the following transitions are allowed in the electronic emission spectrum of a hydrogenic…

A:

Q: Consider a particle trapped in a iD box with zero potential energy with walls at x = 0 and x = L.…

A:

Techniques and applications of quantum theory

Quantum theory, often known as quantum physics, is the foundation of modern physics and encompasses the nature and behavior of matter and energy at the atomic and molecular levels. As the exact nature and behavior of atomic and subatomic particles are impossible to determine, the laws of classical physics do not apply to this discipline. As a result, quantum field theory is primarily based on assumptions and probabilities.