Quantum Mechanics Square Well Potential Problem

[icantsee99]

Homework Statement

A beam of neutrons (m=1.675x10^-27kg) is incident on a nucleus. Consecutive transmission maxima are observed for beam energies of 1.15, 23.656, and 50.254 MeV. Treating the nucleus as a one-dimensional square-well potential:
(a) What is the width of the potential? (ans. 10 fm)
(b) What is the depth of the potential? (ans. 10 MeV)
The observations are related to the Ramsauer-Townsend Effect

Homework Equations

E = (n²h²)/(8ma²)) -V₀

The Attempt at a Solution

I plugged in the mass and energies into the equations, using n=1 for E = 1.15 MeV and n=2 for E = 23.656 MeV. I ended up with

(3.51x10⁴⁰)a²=-V₀
(1.81x10⁴¹)a²=-V₀

I know that I need another equation, but I don't know what to use. We also never learned the Ramsauer-Townsend Effect in class, so I'm not sure how to apply it. Any input would be appreciated!

 

[vela]

The Attempt at a Solution

I plugged in the mass and energies into the equations, using n=1 for E = 1.15 MeV and n=2 for E = 23.656 MeV. I ended up with

(3.51x10⁴⁰)a²=-V₀
(1.81x10⁴¹)a²=-V₀

I know that I need another equation, but I don't know what to use. We also never learned the Ramsauer-Townsend Effect in class, so I'm not sure how to apply it. Any input would be appreciated!

Check your algebra. The solution to those two equations is a=0, V₀=0.