# De Broglie problem

## 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?

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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.

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 $$L=\sqrt{\frac{\pi\hbar\lambda{c}}{4m}}$$

Last edited:
Shooting Star
Homework Helper
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...