What is the width of a square well if its ground-state energy is 2.50 eV?

[meaghan]

Homework Statement

An electron is bound in a square well of depthU0=6E1−IDW.

What is the width of the well if its ground-state energy is 2.50 eV ?

Homework Equations

En = h²n²/8mL²

The Attempt at a Solution

I used n = 1
so I get:
25eV*1.6*10^-19 = h²/8*9.11*10^-31*L²

I got L = .388 nm. It wasn't correct. I ignored the depth part at the beginning since I thought it was irrelevant, but it might not be

 

[DrClaude]

U0=6E1−IDW.

I don't understand what that means.

Homework Equations

En = h²n²/8mL²

That equation is only valid for an infinite square well.

 

[JR_R]

Oh man, this was one of my homework problems (assigned on Monday) too.

You've got [U₀=6E_(1−IDW)]. "IDW" I'm pretty sure means Infinite-Depth Well. This is a finite-depth well so you cannot use infinite-depth equations, but this provided equation gives you a way to apply IDW equations to the FDW.

In practical terms - what they should have included in the problem - is that we can treat [U₀=6E_(1−IDW)] as [U₀=6E_∞].

This is where I don't know where to go. So I sacrificed my own problem to the "give up" button, took my own answer, divided it by my U₀, multiplied it by yours and then put it into the IDW equation. What I got was L = 0.3064 nm. Maybe that will work.

I still have no idea why they thought this was a good problem. I will be writing complaints and talking to my professor.

 

[JR_R]

Belay that. I asked my professor and this is the real answer:

U₀ is the depth of the finite well; E_(1−IDW) is the depth of the infinite well (roll with it). With this equation you find that [E₁ = 0.625E_(1−IDW)] - how you're supposed to figure this out I'm not sure, but you have to to solve the problem.

E1=0.625E_(1−IDW)=2.5eV

E_(1−IDW)=(2.5eV)/0.625=h²n²/8mL²

with n=1 and m=9.11*10^-31kg, and remembering to convert eV to J

L=0.306596nm (with sigfigs, 0.307)

I used this solution to confirm with my numbers and it worked out. I'm still going to report it as a bad problem, though, because at least in my course we didn't cover this in lecture and the textbook *does* have it but in a very roundabout way that a lot of people probably wouldn't catch.