How Much Energy Does an Electron Need to Tunnel Through a Barrier?

[tricky1]

Homework Statement

An electron approaches a potential barrier 10eV high and 0.5nm wide. If the electron has a 1%chance of tunneling through, what must be its energy?

Homework Equations

Transmission probability = [C/A]^2= [ 1 + (U^2 sinh^2(mu alpha))/(4E(U-E))]^-1


where U=potential=10eV
E=energy of electron
mu=sqrt(2m(U-E)/hbar^2)
alpha = width of box = 0.5 nm

The Attempt at a Solution

I've substituted everything in and fiddled for ages but I really can't rearrange to make E the subject of this formula. can anyone help?

 

[malawi_glenn]

What have you tried? Show us.

And have you considered the possiblity to solve this numerically?