Question

Electrons are fired at a rectangular potential energy barrier, once every 197 ms. If the barrier is 2.55 nm thick and has a height that exceeds the energy of the incident electrons by exactly 537 meV, how long on average would you expect to wait for one electron to pass through the barrier?

Electrons are fired at a rectangular potential energy barrier, once every 197 ms. If the barrier is 2.55 nm thick and has a height that exceeds the energy of the incident electrons by exactly 537 meV, how long on average would you expect to wait for one electron to pass through the barrier? average wait

Answer 1

Tunneling probability is given by

Pre-41 V2m(V)

Where V - E = 537 meV

L = barrier thickness = 2.55 nm

h = planck's constant = 6.626 x
10-34 JS
= 4.136 x
10-15evs

m = mass of electron = 9.11 x
10-31 kg
= 0.511 MeV /

Therefore
4 Pre- 2.55 (0.01 (740.82 4.136
​​
=e-981.85

Thus out of $e^{981.85}$ electrons only one electron will tunnel through barrier. Thus time taken to tunnel one electron = 0.197 x $e^{981.85}$ = $10^{426}$ seconds

Thus we will have to wait for $10^{426}$ seconds for one electron to tunnel.