Tunneling Time and Probability of an Electron in a Square Well

Imagine an electron trapped in a well that has walls that are 5nm thick and 10eV high and is 10nm wide. calculate the probability of tunneling for an electron with 0.5eV of kinetic energy. Now, determine the number of times the electron would hit a wall each second. using these two pieces of information determine how long it would take for there to be a 50% probability that the electron has already tunneled out. (imagine this as if you had a large number of these wells and you observed that at time, T, 50% of them were empty.

Solution Preview

After each collision with a wall, the electron has a probability of e^(-kappa T) of tunneling out, where
T = 5 nm is the thickness of the wall,

kappa = sqrt(2m(V0-E))/hbar

is the tunneling coefficient, m = 9.11 * 10^-31 kg is the mass of the electron, V0 = 10 eV is the height of the walls, and E = 0.5 eV is the kinetic energy of the electron. Plugging in the numbers in SI units, we have

We calculate the tunneling probability of an electron of given kinetic energy in a square well of given dimensions as well as the expected time for the electron to escape from the well.

A Hydrogen atom and a Helium atom each with 4 eV of KE approach a thin barrier 6 MeV high which has the greater probability of tunneling through the barrier? Explain.

Hydrogen atom
The radial probability density for an electron is r2R2(r). That means that the probability of finding an electron at a certain radius r within a radial thickness dr is dr* r2R2(r) for an infinitely thin shell and approximately r* r2avg R2(ravg) for a shell of finite thickness r.
The quantity ravg is some average

Draw the Lewis structure for each of the following molecules or ions, and predict their electron-domain and molecular geometries.
1) PF3
what is PF3's electron-domain geometry?
Linear
Trigonal planar
Tetrahedral
Trigonal bipyramidal
Octahedral
what is PF3's molecular geometry?
Linear
Bent
Trigona

Please see the attached file. Also, please show all solution details. Thank you.
German physicist Werner Heisenberg related the uncertainty of an object's position (deltax) to the uncertainty in its velocity deltav.
The mass of an electron is 9.11 x 10-31 kg.
What is the uncertainty in the position of an electron moving at 9

I am given three unnormalized wavefunctions for the system:
psi(x) = 100e^x for x<-4
psi(x) = 0.73 cos[(pi)x/40] for-44
I need to determine the probability of the wavefunction vs. x for this system from x=-10 to x=10 so that I can plot it. I have to comment on the probability of fin

Given a Nanowire with cross sectional dimensions of 10 nm x 10 nm, what momentum would an electron in the ground state need in order to possess the same energy as a stationary electron
(zero momentum) in the n=1,2 state?
I need step-by-step solution please.

An electron is placed in a constant electric field of magnitude 800 N/C. What is the acceleration of the electronand the electromagnetic power radiated by the electron?
I'm not sure how to set it up. Can you help?