Question

a beam of electrons with kinetic energy 106 eV is incident on a 100 eV deep potential well of width L. Is there any value of L that will lead to a 50% reflection ?

Answer #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...

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)

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%.

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

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.

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, 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.)

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) Electrons with an energy of 0.842 eV are incident on a double
slit in which the two slits are separated by 40.0 nm.
What is the speed of these electrons?
_______ m/s
b) Electrons with an energy of 0.842 eV are incident on a double
slit in which the two slits are separated by 40.0 nm.
What is the de Broglie wavelength (in nanometers!) of these
electrons?
_______ nm
c) Electrons with an energy of 0.842 eV are incident...

An infinitely deep square well has width L = 2.5 nm.
The potential energy is V = 0 eV inside the well
(i.e., for 0 ≤ x ≤ L). Seven electrons
are trapped in the well.
1) What is the ground state (lowest) energy of this seven
electron system in eV?
Eground =
2) What is the energy of the first excited state of the system
in eV?
NOTE: The first excited state is the one that has the lowest...

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