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

• meaghan
In summary, the homework statement says that an electron is bound in a square well of depth U0=6E1−IDW. The width of the well is given by theground-state energy of the electron, which is 2.50 eV. If n=1, then h2/8*9.11*10-31*L2=25eV. L=0.306596nm if sigfigs are used.

## 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 ?

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

meaghan said:
U0=6E1−IDW.
I don't understand what that means.

meaghan said:

## Homework Equations

En = h2n2/8mL2
That equation is only valid for an infinite square well.

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.

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.

## 1. What is an infinite well width?

An infinite well width is a theoretical concept in quantum mechanics where a particle is confined within an infinitely wide potential well. This means that the particle is not able to escape the well, and its energy is quantized.

## 2. What is the significance of an infinite well width?

An infinite well width is important in understanding the behavior of particles in quantum systems. It can help us understand the relationship between a particle's energy and its position within a potential well, and it has implications for various physical phenomena such as light emission and tunneling.

## 3. How is an infinite well width different from a finite well width?

The main difference between an infinite well width and a finite well width is that in an infinite well, the particle is confined within the well and cannot escape, while in a finite well, the particle can escape if it has enough energy. Additionally, the energy levels in an infinite well are discrete and evenly spaced, while in a finite well they can be non-uniformly spaced.

## 4. What are the applications of an infinite well width?

An infinite well width has various applications in physics, such as in the study of semiconductors, quantum dots, and quantum wells. It is also used in understanding the behavior of particles in potential barriers and quantum confinement, and it has implications for technologies such as lasers and transistors.

## 5. Can an infinite well width exist in the real world?

An infinite well width is a theoretical concept that does not exist in the real world. However, it can be approximated in certain physical systems, such as in a graphene sheet or in a quantum dot, where the particle is confined in all three dimensions. In these cases, the well width is considered to be effectively infinite for the confined particle.