How Does Electron Kinetic Energy Affect Barrier Penetration Probability?

[r-dizzel]

uncertain about this??

evenin' all!
wonder if anyone can help...

the question is this-

(sorry by the way if this is wrong place to post this, bit of a newbee!)

an electron has 100eV of kinetic energy, its incident on a potential barrier of height 110eV. At what distance x does the probability of finding the electron fall to 1/e of its value at x = 0? compare this with what might of be expeceted from Heisenbergs uncertainty principle.

ive calculated the wavefunctions in and before the boundary but don't really understand what the questions asks "falls to 1/e of its original value"? surely e on its own is meaningless?

the final part about the Heisenbergs unc princ i get but i thought i'd complete the questions.

would really appreciate any help

over and out

r dizzel

 

[lpfr]

The solution of Shrödinger function decreases as:
$$\Psi= Ae^{-\beta x}$$
where
$$\beta^2={2M(E_1-E_2) \over \hbar}$$
M is the electron mass and the energies must be in SI units.