Answered Essay: Il- 6. Simplest Quantum System -Particle in a Box (Oxtoby 4.6) [21(a) The Schrõdinger

Il- 6. Simplest Quantum System -Particle in a Box (Oxtoby 4.6) [21(a) The Schrõdinger equation for a particle of mass m constrained to move on a circle of radius a is 2I d02 where I ma2 is the moment of inertia and 0 is the angle that describes the position of the particle around the ring. Show that the solutions to this cquation are where n= (21E)112/h. Argue that the appropriate boundary condition is ψ(θ)-ψ(9 + 2π) and use this to show that =21- n-0, tl, ±2,..。 [2(b) Now, lets see how particle on a ring quantum model you just solved in [2](a) can help us quantitatively understand the conjugated π-bonds in benzene C6H6. Six of the electrons from benzene C6H6 form a delocalized conjugated π-bond. We will model it as particle on a ring with ring radius a particle (electron) mass m, and moment of inertia ma-. After obtaining the energy diagram, we will then fill in these 6 electrons. Please estimate the energy (in Joule) of a single delocalized π electron in the specific state shown above. Assume the radius a=0.15nm (Hint just like the quantum square or PIB-1D problem, one can estimate the quantum number or which state from the number and structure of the nodes)

Il- 6. Simplest Quantum System -Particle in a Box (Oxtoby 4.6) [21(a) The Schrõdinger equation for a particle of mass m constrained to move on a circle of radius a is 2I d02 where I ma2 is the moment of inertia and 0 is the angle that describes the position of the particle around the ring. Show that the solutions to this cquation are where n= (21E)112/h. Argue that the appropriate boundary condition is ψ(θ)-ψ(9 + 2π) and use this to show that =21- n-0, tl, ±2,..。 [2(b) Now, let’s see how “particle on a ring” quantum model you just solved in [2](a) can help us quantitatively understand the conjugated π-bonds in benzene C6H6. Six of the electrons from benzene C6H6 form a delocalized conjugated π-bond. We will model it as ‘particle on a ring” with ring radius a particle (electron) mass m, and “moment of inertia” ma-. After obtaining the energy diagram, we will then fill in these 6 electrons. Please estimate the energy (in Joule) of a single delocalized π electron in the specific state shown above. Assume the radius a=0.15nm (Hint just like the “quantum square” or PIB-1D problem, one can estimate the quantum number or which state from the number and structure of the nodes)

Expert Answer

Answer
Buy Essay
Calculate your paper price
Pages (550 words)
Approximate price: -

Help Me Write My Essay - Reasons:

Best Online Essay Writing Service

We strive to give our customers the best online essay writing experience. We Make sure essays are submitted on time and all the instructions are followed.

Our Writers are Experienced and Professional

Our essay writing service is founded on professional writers who are on stand by to help you any time.

Free Revision Fo all Essays

Sometimes you may require our writers to add on a point to make your essay as customised as possible, we will give you unlimited times to do this. And we will do it for free.

Timely Essay(s)

We understand the frustrations that comes with late essays and our writers are extra careful to not violate this term. Our support team is always engauging our writers to help you have your essay ahead of time.

Customised Essays &100% Confidential

Our Online writing Service has zero torelance for plagiarised papers. We have plagiarism checking tool that generate plagiarism reports just to make sure you are satisfied.

24/7 Customer Support

Our agents are ready to help you around the clock. Please feel free to reach out and enquire about anything.

Try it now!

Calculate the price of your order

Total price:
$0.00

How it works?

Follow these simple steps to get your paper done

Place your order

Fill in the order form and provide all details of your assignment.

Proceed with the payment

Choose the payment system that suits you most.

Receive the final file

Once your paper is ready, we will email it to you.

HOW OUR ONLINE ESSAY WRITING SERVICE WORKS

Let us write that nagging essay.

STEP 1

Submit Your Essay/Homework Instructions

By clicking on the "PLACE ORDER" button, tell us your requires. Be precise for an accurate customised essay. You may also upload any reading materials where applicable.

STEP 2

Pick A & Writer

Our ordering form will provide you with a list of writers and their feedbacks. At step 2, its time select a writer. Our online agents are on stand by to help you just in case.

STEP 3

Editing (OUR PART)

At this stage, our editor will go through your essay and make sure your writer did meet all the instructions.

STEP 4

Receive your Paper

After Editing, your paper will be sent to you via email.

× How can I help you?