Solving the De Broglie Problem: Calculating Length of a 1-D Box

[psingh]

Homework Statement

What is the length of a one-dimensional box in which an electron in the n=1 state has the same energy as a photon with a wavelength of 500 nm

Homework Equations

E=h^2/8mL^2 and E=hc/lambda

making it
L=sqrt( (h*lambda)/(8cm) )

The Attempt at a Solution

I plugged in for those numbers and did not come out with the correct number. any suggestions?

 

[S.P.P]

Are you sure that 8 should not be a 4?

 

[pam]

The eightfold way is right here. 1/8=(L/2)^/2.
I think your first h should be hbar.

 

[eys_physics]

Hey
The energy if the first state of an indefinite one-dimensional box is:
$$E=\frac{\pi^{2}\hbar^{2}}{2mL^{2}}$$
Where m is the mass of the particle and L is the length of the box.
The photon has the energy given by
$$E=\hbar\omega=\frac{2\pi\hbar{c}}{\lambda}$$
Where $$\lambda$$ is the wave length.
And therefore the length L is $$L=\sqrt{\frac{\pi\hbar\lambda{c}}{4m}}$$

 

[Shooting Star]

And therefore the length L is $$L=\sqrt{\frac{\pi\hbar\lambda{c}}{4m}}$$

Which is wrong. It should be $$\sqrt{\frac{\pi\hbar\lambda}{4mc}$$, which is identical to what the OP psingh had written correctly. Replacing $h$ by $2\pi\hbar$ won't do any good.

Perhaps the OP made some arithmetical mistake...