Question

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%.

Answer #1

An
electron with an energy of 5.5 eV approaches a potential barrier of
height 6.1 eV and thickness of 1nm. What is the relative
probability that the electron passes through the barrier? What
barrier height should be used to decrease the relative probability
by a factor of 100?

An electron having total energy E = 3.40 eV approaches
a rectangular energy barrier with U = 4.10 eV and
L = 950 pm as shown in the figure below. Classically, the
electron cannot pass through the barrier because E <
U. Quantum-mechanically, however, the probability of
tunneling is not zero.
(a) Calculate this probability, which is the transmission
coefficient. (Use 9.11 10-31 kg for the mass
of an electron, 1.055 10-34 J · s for ℏ, and
note that there are...

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 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

Suppose a beam of 4.00 eV protons strikes a potential energy
barrier of height 6.20 eV and thickness 0.560 nm, at a rate
equivalent to a current of 1150 A. (a) How many years would you
have to wait (on average) for one proton to be transmitted through
the barrier? (b) How long would you have to wait if the beam
consisted of electrons rather than protons?

Suppose a beam of 5.10 eV protons strikes a potential energy
barrier of height 5.80 eV and thickness 0.810 nm, at a rate
equivalent to a current of 980 A. (a) How many
years would you have to wait (on average) for one proton to be
transmitted through the barrier? (b) How long
would you have to wait if the beam consisted of electrons rather
than protons?

Suppose a beam of 4.60 eV protons strikes a potential energy
barrier of height 6.10 eV and thickness 0.530 nm, at a rate
equivalent to a current of 1190 A. (a) How many
years would you have to wait (on average) for one proton to be
transmitted through the barrier? (b) How long
would you have to wait if the beam consisted of electrons rather
than protons?

Suppose a beam of 5.10 eV protons strikes a potential energy
barrier of height 6.00 eV and thickness 0.840 nm, at a rate
equivalent to a current of 860 A. (a) How many
years would you have to wait (on average) for one proton to be
transmitted through the barrier? (b) How long
would you have to wait if the beam consisted of electrons rather
than protons?

A 1.4 eV electron has a 10-4 probability of tunneling
through a 2.5 eV potential barrier. What is the probability of a
1.4 eV proton tunneling through the same barrier?

A 1.5 eV electron has a 10-4 probability of tunneling through a
2.0 eV potential barrier. What is the probability of a 1.5 eV
proton tunneling through the same barrier?

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