electron in a box... how to find the length of the box?

[phatj]

Can anyone give me a tip? I just need a step in the right direction...

An electron confined in a one-dimensional box is observed, at different times, to have energies of 64.0 eV, 100. eV, and 144 eV. What is the length of the box?

 

[MrDudeMan]

.

 

[jagec]

How do you know the electron's actually in the box? You change the outcome when you open it!

 

[phatj]

Originally posted by: MrDudeMan
lol wrong forum first of all...

also, do your own homework. this is a very easy probability problem, and i could help you with it, but since you offered no work of your own or even the slightest hint that you have attempted it, im not going to tell you jack squat.

my work:

En= (h^2 n^2) / (8 * m * L^2)

Take the first two energies

64eV * 1.6E-19 = ((6.63E-34)^2 (8)^2 ) / (8 * 9.11E-31 * L^2)

1.024 E-17 J = 1 / ((3.86E-33) * L^2)

L^2 = 3.76E-19

L=6.139E-10

L= 0.6139nm


L comes out to be the same when En=100eV (with n=10 im guessing) and En=144 (with n=12 im guessing)

However, that answer is incorrect!! I'm going beserk!

 

[MrDudeMan]

rearrange the shrodinger equation to specify the 2nd derivative of the wavefunction at any point as a function of the potential and the energy as a function of the wavefunction in x.

then, find the equation which gives the lowest allowable energy...its something like (pi^2*hbar^2)/(2*L^2*m) where L is the length of the box. that is off the top of my head so it might be wrong, but i think it is right. also, you can find the nth Energy state with another equation, En=(n^2*pi^2*hbar^2)/(2*L^2*m). ok yeah i just reaffirmed it...the first equation i gave you is right because it is just n = 1. so anyway, that should help a lot.

 

[MrDudeMan]

Originally posted by: phatj

Originally posted by: MrDudeMan
lol wrong forum first of all...

also, do your own homework. this is a very easy probability problem, and i could help you with it, but since you offered no work of your own or even the slightest hint that you have attempted it, im not going to tell you jack squat.

my work:

En= (h^2 n^2) / (8 * m * L^2)

Take the first two energies

64eV * 1.6E-19 = ((6.63E-34)^2 (8)^2 ) / (8 * 9.11E-31 * L^2)

1.024 E-17 J = 1 / ((3.86E-33) * L^2)

L^2 = 3.76E-19

L=6.139E-10

L= 0.6139nm


L comes out to be the same when En=100eV (with n=10 im guessing) and En=144 (with n=12 im guessing)

However, that answer is incorrect!! I'm going beserk!

what is the answer given?

 

[phatj]

no answer given. However, I get "incorrect answer" when I input it online

 

[MrDudeMan]

you dont need to convert to joules to do this calcuation. you can use units in eV.

 

[phatj]

how do I know what n is? I assume n=8 when energy is 64eV (just because it is a perfect square, same with 100 and 144). Is that where my error is? Because using 3 different equations I am attaining the same solution

 

[Evadman]

The probabilities colapse when you open the box! How dare you open the box!

 

[MrDudeMan]

En = n^2*E1 where E1 is the lowest energy state. see if that helps.

 

[MrDudeMan]

also, En=(hbar^2*k^2)/(2*m) where k=(n*pi)/L. honestly, i cant remember if that helps. let me work on this for a second...


edit: are you taking this quiz on webct? and did you give all of the information in the problem?

 

[phatj]

ehhh no luck. Perhaps there is a problem with the website.... because i am almost certain im doing this correctly.

I get either L = .0613nm or L=.0767nm depending which values for n I use. neither are correct apparently

 

[phatj]

this isn't a quiz.. just bonus homework but the questions on the bonus HW is often on the quiz which is the day after tomorrow. So it is k,ind of essential i know how to solve this problem

 

[phatj]

and yes I copied and pasted the probelm. Seems like a crap problem to me.

 

[MrDudeMan]

ok, i may be wrong, but my answer is 3.7611*10^-13 m, or .37611 picometers, or 376.11 fm.

 

[MrDudeMan]

going to bed...ill check back in the morning.

 

[msparish]

The problem is not solvable according to the information provided. Remember you get (from the Shrodinger Equation)

E=h^2*n^2/(8*m*L^2)

From the problem, you have two unkowns (both n and L) with only one equation. You cannot know what the ground state energy is (because to have that you would need to know L). Therefore, you cannot deduce what the values for n are from the given energies. Obviously you don't know L, because that is what you are trying to solve for.

As far as your set up goes, (assuming you did the math correctly) everything looks fine if n actually was 8, 10, and 12. In addition, all of your answers should be the same because the energy level is coupled to the actual energy...you just don't know what they are so you can't solve.

 

[phatj]

well the answer is posted in 30 minutes so ill follow up...

 

[phatj]

Originally posted by: phatj
well the answer is posted in 30 minutes so ill follow up...

Here's the solution posted. (For this class, solutions ALWAYS contain different numbers but all the same equations apply. For example, the difference between the question I had to answer and the solution posted is only the energy: For me it was 64ev, 100eV, and 144eV. Solution uses levels of 12eV, 27eV, and 48eV).

Here's the solution (it's an image cuz I had to copy/paste a .pdf)

 

[msparish]

Like I said, that is still a poor solution. There are other values for the energy levels that would work (e.g. 20, 30, and 40).

 

[phatj]

yea that's what I thought too -- i think this question is somewhat MOOT!!

 

[drinkmorejava]

lol, AP test on monday? I'm so ready to get raped after the Comp Sci AB exam

 

[WhoBeDaPlaya]

I might be wrong (took my advanced semicon and advanced FET classes about 3 years ago), but looks like you have two unknowns to solve for. The solution looks pretty darned arbitrary in the sense that other values of n would work.

 

[tranceport]

Don't you guys know anything???


You use a measuring tape of course!!!!