Electrons inside a carbon nanotube - Quatum Mechanics

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Homework Help Overview

The discussion revolves around the behavior of electrons within a carbon nanotube, specifically modeling them as a one-dimensional "particle in a box." The original poster is attempting to determine the minimum speed of an electron given the length of the nanotube.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • The original poster attempts to apply the kinetic energy formula to find the speed of the electron but questions why their approach yields an incorrect answer. They also seek clarification on the appropriate equations to use in this context.

Discussion Status

Some participants provide guidance on the correct energy equation for a particle in a box and suggest that the original poster may have made an error in applying the length variable. There is an acknowledgment of common mistakes in calculations, indicating a supportive atmosphere for learning.

Contextual Notes

The original poster's calculations are based on the assumption of a specific length for the nanotube and the properties of electrons, which are being discussed in the context of quantum mechanics.

Feodalherren
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Homework Statement


Electrons inside a carbon nanotube can be approximated as a one dimensional "particle in a box". If the nanotube is 3 micrometers long, what is the minimum speed of an electron inside the tube?

Homework Equations


The Attempt at a Solution



The minimum occurs as n=1 so therefore

[itex]K=\frac{h^{2}}{8M_{e^{-}}(3E-6)}= 2.01E-32J[/itex]

If I use 1/2 mV^2 to find V I get the wrong answer. Why can't I use it and what should I use instead?
 
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The lowest energy state in a particle in a box is

[tex] E_n = \frac{h^2}{8m_eL^2}[/tex]

If you used the equation as you wrote it, you didn't square your L.

Then you can use the

[tex] E = \frac{1}{2}mv^2[/tex]

formula to solve for v.
 
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Gah it's always something stupid like that. Thanks.
 
No worries! I've done 28328348238 stupid things like that over the years.
 

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