Question

A beam of electrons is incident on a barrier 6 eV high and.2nm wide.Find the energy they should have if 1.00percent of them are to get through thebarrier.The equations that have to be used arePlease help

Answer 1

The transmission coefficient is 1% = 0.01
0.01 = e^{-2k₂ L}
- 2 K₂ L =ln ( 0.01 )
- 2 K₂L= -4.6051
K₂ = 4.6051/ 2 (0.2 x10^{- 9})
=1.1513x 10¹⁰
√[2m(U -E ) = h(bar)1.1513x 10¹⁰
[2m(U -E )= [h(bar)1.1513x 10¹⁰]^{2
(U -E )= [h(bar)1.1513x1010]2/ 2m}
here m = 9.1 x 10^-31 kg, h (bar) = 1.0536 x10^-34
U - E = 8.0756x10^-19J
In eV
U - E=8.0756x10^-19J( 1eV/ 1.6x10^-19 J )
= 5.0473eV
E = U - 5.0473eV
= 6eV -5.0473eV
= 0.9526eV