The particle on a ring is a useful model for the motion of electrons around the porphine ring, the conjugated macrocycle that forms the structural basis of the haem group and the chlorophylls; see the structure of the porphine molecule below. -NH HN- We may treat the structure as a circular ring of radius 440 pm, with 22 electrons in the conjugated system moving along the perimeter of the ring. Assuming that, in the ground electronic configuration of the molecule, each state is occupied by two electrons, calculate:

The particle on a ring is a useful model for the motion of electrons around the porphine ring, the conjugated macrocycle that forms the structural basis of the haem group and the chlorophylls; see the structure of the porphine molecule below. -NH HN- We may treat the structure as a circular ring of radius 440 pm, with 22 electrons in the conjugated system moving along the perimeter of the ring. Assuming that, in the ground electronic configuration of the molecule, each state is occupied by two electrons, calculate:

Chemistry

10th Edition

ISBN:9781305957404

Author:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste

Publisher:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste

Chapter1: Chemical Foundations

Section: Chapter Questions

Problem 1RQ: Define and explain the differences between the following terms. a. law and theory b. theory and...

See similar textbooks

Related questions

Q: Write the term symbols for the 5f12 electron configuration. Show all work.

A: The term symbol is given below.Explanation:

Q: APPLY KINECTIC ENERGY, POTENTAIL ENERGY, MOMENTUM QUANTUM OPERATORS ON THE FOLLOWING WAVE-FUNCTION…

A: To apply the kinetic energy, potential energy, and momentum quantum operators to the wave function…

Q: For a particle in a box of length L and in the state with n = 5, at what positions is the…

A: Given ,length of box = Lvalue of n = 5Objective :(a) Determine position of maximum probablity…

Q: The electronic structure of one-dimensional chain of sodium (Na) atoms can be approximately…

Q: The orange color of carrots and orange peel is due mostly to b-carotene, an organic compound…

A: The concentration of β-carotene in the oil from orange peel has to be determined by an experiment.

Q: The wave function for the ground state of the harmonic oscillator is %0 (2) = Ce-mw/(2A)|z² where C…

A: In the given question the ground state of the hormonic oscillator is given in unnormalised form,…

Q: Neglecting electron-electron repulsion, write down the singlet and triplet excited states of with…

Q: Determine the value of the orbital, L, spin, S, total angular momentum J and g, for the ions Pr³+…

A: The given ions are Pr^3+ and Yb^3+.Here L is orbital angular momentum..S is Spin angular momentum.J…

Q: Please answer both questions!! Please make sure it's handwritten and legible!!!

A: Approach to solving the question: Detailed explanation: Examples: Key references: read macquirre…

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

Q: Write down the normalized determinantal wave function (slater determinant) of a He atom at its…

A: To find the normalized slater determinant of the ground state of the He atom.Also to prove that the…

Q: Calculate the expectation value of the radius (r) at which you would find the electron if the H atom…

Q: Consider an excited state configuration for He, 1s¹ 2p¹. (a) Find all the possible term symbols for…

Q: What is the significance of the y-intercept of a Rydberg plot?

A: An excited electron within a hydron atom moves from a low energy level (ground state) to a higher…

Q: (d) Principles of quantum mechanics: Topics 7D - 7F in Atkins The three basic modes of motion of…

A: In quantum mechanics, the three basic modes of motion—translation, vibration, and rotation—are…

Q: Please answer this question! Make sure its handwritten and legible!!

A: Part 2: ExplanationStep 1: Determine Energy Levels\[ E_{n,J} = w \left( n^2 + \frac{1}{2} \right) +…

Q: 8. Do the linear momentum operator px and angular momentum operator Lx commute. Can the velocity in…

Q: 6. For a particle in a box of length L, what is the probability the particle will exist between x =…

A: To calculate the probability, we would use wavefunction of particle in 1-d box of length L . The we…

Q: Where are the nodes in the wavefunction for a particle confined to a box with 0 < x < a and n=3?

A: Wave function for a particle in a box with 0 < x < a and n=3 No of nodes = to be determined.…

Q: 5. (McQuarrie 9-25) Show that the atomic determinantal wave function, 1 1sa (1) 1sẞ(1) V(r1, r2)= √2…

A: The question asks to prove that a given atomic determinant wavefunction is normalized when the 1s…

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

Q: Bohr’s model can be used for hydrogen-like ions—ions thathave only one electron, such as He + and…

A: To find: Reason for the application of Bohr model for He+ ion and not for neutral He Relationship…

Q: A certain system with a wavefunction v is the linear combination: where yl and y2 are energy…

A: We have to calculate the probability that the system will be observed to be E1 and E2:

Q: Construct the wavefunction V(r, 0, ø) for an H atoms' electron in the state 2p,. Please note that in…

A: finding the WAVEFUNCTION of 2px orbital of HYDROGEN ATOM using quantum mechanics.

Q: Imagine a particle free to move in the x direction. Which of the following wavefunctions would be…

Q: Assume that a certain process puts the electron in a state that is characterized by the term symbol…

Concept explainers

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.

Question

The particle on a ring is a useful model for the motion of electrons around the porphine ring, the
conjugated macrocycle that forms the structural basis of the haem group and the chlorophylls;
see the structure of the porphine molecule below.
-NH
N:
HN-
We may treat the structure as a circular ring of radius 440 pm, with 22 electrons in the
conjugated system moving along the perimeter of the ring. Assuming that, in the ground
electronic configuration of the molecule, each state is occupied by two electrons, calculate:
a. the angular momentum and energy of an electron in the highest occupied level, and
b. the frequency of radiation that can induce a transition between the highest occupied and
lowest unoccupied levels.

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

This is a popular solution!

SEE SOLUTION Check out a sample Q&A here

Step 1

VIEW

Step 2

VIEW

Step 3

VIEW

Trending now

This is a popular solution!

Step by step

Solved in 3 steps with 3 images

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

Techniques and Applications of Quantum Theory

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, chemistry and related others by exploring similar questions and additional content below.

Similar questions

Consider a 1D particle in a box confined between a = 0 and x = 3. The Hamiltonian for the particle inside the box is simply given by Ĥ . Consider the following normalized wavefunction 2m dz² ¥(2) = 35 (x³ – 9x). Find the expectation value for the energy of the particle inside the box. Give your 5832 final answer for the expectation value in units of (NOTE: h, not hbar!). In your work, compare the expectation value to the lowest energy state of the 1D particle in a box and comment on how the expectation value you calculated for the wavefunction ¥(x) is an example of the variational principle.
3. Prove that angular momentum of a particle confined to the xy palne is quantized 4. Neutrons have no electric charge, so they do not interact with the atomic electrons. Hence, they are very penetrating (e.g.,typically 10 cm in lead). Neutron diffraction was proposed in 1934, to exploit de Broglie's hypothesis about the wave nature of matter. Calculate the momentum and kinetic energy of a neutron whose wavelength is comparable to atomic spacing (1.8×1010 m)
1. The angular portions of the wave functions for the px and dxz orbitals of the hydrogen atom are linear combinations of the spherical harmonics and are given by the expressions below. 3 YP. = √(x²+x¹) = -sin coso 4T Wd₂ = 1/2 (Y/² + X/₂ ¹) = eigenfunctions of 15 4π These combinations are chosen to yield real functions. Are these functions a Ĺ sincoscoso -iħ. do ?
What are the possible term symbols for the 1s 2s configuration of helium? o 's only 15 and 3p O 2s only O 1S and 3S
How are the wave functions of the two electrons in a He atom constructed from the individual orbital and spin wave functions? Write down the antisymmetric wave function of the configuration in determinantal form that contains both orbital and spin components for Ms=1 in He.
19. List the quantum numbers of all states in the 4d subshell of hydrogen in the (n, l, me, ms) basis and in the (n, l, j, mj) basis.
Using a simple particle-in-a-box model for the multiple bonding in 1,2-butadiene 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 Å, so this interval is from x1 = 2.06 Å to x2 = 2.16 Å). 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 |Ψ(x0)|^2 ∆x, where x0 is evaluated in the middle of the range from x1 to x2.
Consider a single particle with rest mass m residing in a one-dimensional space, x. This particle experiences a potential energy V(x) = ∞ for x a, and a potential energy V(x) = 0 for 0 < x < a. The solutions to the Schrödinger Equation for this system are 12. 2 Vn(x) : sin a where n is the state's quantum number. Show that the ground state wave function is normalized.
Calculate the energies of an electron in the fourth, fifth, and sixth energy levels of the Bohr nydrogen atom. Calculate the angular momenta of an electron in the fourth, fifth, and sixth energy evels of the Bohr hydrogen atom.