Minimum energy needed for a positrons to tunnel

[ElectricEel1]

Homework Statement

10^12 positrons of the same kinetic energy are incident on 10eV, 1nm barrier. What is the minimum kinetic energy the positrons need before any of them can penetrate the barrier?

Homework Equations

p_T = e^(-2*a*L)
a = (sqrt(2m(V_0-E))/hbar

The Attempt at a Solution

For other problems I've plugged numbers into these equations to find non zero probabilities but this time I'm not sure how to solve it. I tried setting p_T to zero and rearranging for E but that just ended up as V_0=E.

 

[Orodruin]

Theoretically, they can pass the barrier regardless of their energy. It is just that the probability will be vanishingly small.

What I would guess the problem wants you to do is to figure out when on average one positron will pass.

Can you clarify the question?