Consider a potential energy barrier like that of the figure

Consider a potential energy barrier like that of the figure but whose height U_0 is 7.6 eV and whose thickness L is 0.73 nm. What is the energy of an incident electron whose transmission coefficient is 0.00082? Number Units eV the tolerance is +/-2%

Solution

U₀ = 7.6 eV

L = 0.73 nm

E = U₀ - [ ((hc)² (ln T)) / (32 pi² L² m_ec²) ]

= 7.6 eV - [ (1240² * ln 0.00082) / (32 pi² (0.73 nm)² (0.511 * 10⁶) ]

E = 6.697 eV