MYTUTOR SUBJECT ANSWERS

592 views

How can I derive the energy of an electron using the electron in a box model?

The electron in a box model uses the idea that the energy of the electron and that of a standing wave in a box are analogous. So using your knowledge of standing waves you can derive an equation for the electrons energy.

The equation you need to derive is KE = (n2h2)/(8mL2)

It looks a little daunting and is not something I would memorise. Thankfully the derivation just requires 3 main steps and 3 main equations.

Treat the electron in a box as you would treat a standing wave on a string length L. The boundary conditions are that the wave has nodes at either end of the string. If you start drawing out the possible wavelengths on a string length L you will start to see a relationship emerging between the number of anti-nodes, n, and the wavelength, λ. Thus the allowed wavelengths are λ = 2L / n where n = 1, 2, 3, ...

Now that we have this relation we can use our equations from quantum physics, look for one that might includes λ, in this case λ = h / p.

Now substitue p = mv we have λ = 2L / n  = h / (mv). Which rearranges to v = (hn) / (2Lm). So now we have an equation for the velocity of the electron in terms of L.

Remember we needed to find an expression for the energy, but there is the equation KE = mv/ 2. So by substitution:

KE = (n2h2)/(8mL2)

This equation can model the energies of an electron according to it's energy level in the atom. So the n in the equation represents its energy level, the h is Planck's constant, m is the mass of the electron and L is the the length of the box or the space to which the electron is confined.

Lucile C. GCSE Physics tutor, IB Physics tutor, A Level Physics tutor...

1 year ago

Answered by Lucile, an IB Physics tutor with MyTutor


Still stuck? Get one-to-one help from a personally interviewed subject specialist

13 SUBJECT SPECIALISTS

£24 /hr

Mohammad M.

Degree: General Engineering (Bachelors) - Durham University

Subjects offered:Physics, Maths+ 2 more

Physics
Maths
Chemistry
Arabic

“I am studying Engineering at Durham University. From a very early age I have been fascinated by machines; how they work, how they have developed over time, and how they are useful in society today. I have a keen interest in motors and ...”

£30 /hr

Ravi S.

Degree: Mechanical Engineering (Masters) - Bristol University

Subjects offered:Physics, Maths

Physics
Maths

“Masters Mech eng. student, University of Bristol. Did Physics, Maths + Further Maths. Not free till 19th may due to exams”

£36 /hr

James G.

Degree: Mathematical Physics (Doctorate) - Nottingham University

Subjects offered:Physics, Maths+ 2 more

Physics
Maths
Further Mathematics
.STEP.

“Currently a 3rd year PhD student in Mathematical Physics. I'm very passionate about teaching as well as my subject area. Look forward to hearing from you.”

About the author

Lucile C.

Currently unavailable: for new students

Degree: Mathematical Physics (Bachelors) - Edinburgh University

Subjects offered:Physics, Maths+ 1 more

Physics
Maths
Chemistry

“Hi! I’m a third year student at the University of Edinburgh studying Mathematical Physics. I completed IB with 42 points with 7s in HL Physics and Maths.”

MyTutor guarantee

You may also like...

Posts by Lucile

How can I derive the energy of an electron using the electron in a box model?

How do I derive the indefinite integral of sine?

Other IB Physics questions

Tritium is a radioactive nucleide with a half life of 4500 days, determine the time for 90% of it to decay.

Give the unit of energy, using only the base SI units kg, m and s.

How can an object in circular motion be accelerating when it's at the same speed?

How would I write the binary number 11001 in decimal form?

View IB Physics tutors

We use cookies to improve your site experience. By continuing to use this website, we'll assume that you're OK with this. Dismiss

mtw:mercury1:status:ok