Question

A beam of electrons, each with energy E=0.1V0 , is incident on a potential step with V0 = 2 eV. This is of the order of magnitude of the work function for electrons at the surface of metals. Calculate and graph (at least 5 points) the relative probability |Ψ2|^2 of particles penetrating the step up to a distance x = 10-9 m, or roughly five atomic diameters. (Hint: assume A=1.)

Answer #1

Reflection from a Step with E < V0: A beam of electrons, each
with energy E=0.1V0 , is incident on a potential step with V0 = 2
eV. This is of the order of magnitude of the work function for
electrons at the surface of metals. Calculate and graph (at least 5
points) the relative probability |Ψ#|# of particles penetrating the
step up to a distance x = 10-9 m, or roughly five atomic diameters.
(Hint: assume A=1.)

A beam of 1,000,000 electrons, each with kinetic energy E = 1.0
eV, is incident on a potential barrier with the height V0 = 7.0 eV.
(a) How many electrons in the beam will be transmitted through the
barrier if the barrier width a = 0.25 nm? (b) Answer the same
question if the width is doubled, that is, a = 0.5 nm. (c) Briefly
explain the effect of the barrier width in quantum tunneling, based
on your results in...

A beam of protons, each with energy E=20 MeV, is incident on a
potential step 40 MeV high. Graph using a computer the relative
probability of finding protons at values of x > 0 from x = 0 to
x = 5 fm.
Please do not just copy the answer to this question that has
been posted on Chegg all ready

A beam of particles is incident from the negative x
direction on a potential energy step at x = 0. When
x < 0, the potential energy of the particles is zero,
and for x > 0 the potential energy has the constant
positive value U0. In the region x
< 0, the particles have a kinetic energy K that is
smaller than U0. What should the form of the
wave function be in the region x > 0?

For the arrangement of Figure (a) and Figure
(b), electrons in the incident beam in region 1 have
energy E = 836 eV and the potential step has a height of
U1 = 627 eV. What is the angular wavenumber in
(a) region 1 and (b) region 2?
(c) What is the reflection coefficient?
(d) If the incident beam sends 5.60 ×
105 electrons against the potential step, approximately
how many will be reflected?
(a)

A monoenergetic beam of electrons is incident on a single slit
of width 8.0 Angstroms . A diffraction pattern is formed on a
screen 30 cm from the slit. If the distance between successive
minima of the diffraction pattern is 3.2 cm, what is the energy of
the incident electron? answer is 13 ev, how do you get it? I keep
getting 209 eV

A beam of electrons with energy 150 eV is incident on a sample
of polycrystalline Cu. Given that Cu has a fcc unit cell with a =
3.61 ˚A, find the three smallest Bragg angles at which diffraction
takes place.

An electron beam with energy 0.1 eV is incident on a potential barrier with energy 10 eV and width 20 ˚A. Choose the variant that you think best describes the probability of finding an electron on the other side of the barrier: a) 0; b) <10%; c) 100% d) 200%.

Particles with energy E, are incident from the left, on the
step-potential of height V0 = 2E as shown: a. What are the wave
numbers in the two regions, 1 k and 2 k , in terms of E? b. Write
down the most general solutions for the Schrodinger Equation in
both regions? Identify, with justification, if any of the
coefficients are zero. c. Write down the equations that result for
applying the boundary conditions for the wave functions at...

A beam of electrons with kinetic energy 25 eV encounter a
potential barrier of height 20 eV. Some electrons reflect from the
barrier, and some are transmitted. Find the wave number k of the
transmitted electrons.
You can take U = 0 for x < 0, and U = 15 eV for x > 0

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