Electrons inside a carbon nanotube - Quatum Mechanics

[Feodalherren]

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

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

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?

 

[eprparadox]

The lowest energy state in a particle in a box is

$$E_n = \frac{h^2}{8m_eL^2}$$

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

Then you can use the

$$E = \frac{1}{2}mv^2$$

formula to solve for v.

 

[Feodalherren]

Gah it's always something stupid like that. Thanks.

 

[eprparadox]

No worries! I've done 28328348238 stupid things like that over the years.