Question

1. Calculate the permeability of electrons with energy of 0.1 eV and 0.5 eV respectively when penetrating a positional energy barrier of 1.0 eV in height and 100 pm in length by tunnel phenomenon.
k Attachment image=[2m(V-E)]^1/2
T={1+(e^kL-e^-kL)^2/16ε(1-ε)}^-1 (ε= E/V)
2. Explain the meaning of tunneling covered in the above problem with the wave and explain the difference between classical and quantum mechanics based on it.

Answer 1

Given that

V = 1 eV - height of potential barrier

L - length of potential barrier = 100 pm =

Here

Case 1

case 2

(b)

The process involved here is quantum tunneling.

In case of a potential barrier of barrier potential V and the energy of the particle E, there will be 3 possible scenarios.

E>V

in this case, the particle is a free particle and will go undeviatingly classically and quantum mechanically.

E = V

In this case, the particle will undergo scattering.

E<V

This is the classically forbidden region ie the particle can not cross the barrier in a classical scenario. But quantum mechanically, there is a nonzero probability that the particle can cross through the barrier even if it has less energy. This pheonomena is known as tunneling.