Question

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.

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Answer #1

For tunneling, probabilty at a distance x from the start of barrier is given by

where U is potential = 40MeV=40*1.6*10-13J

E=20MeV=20*1.6*10-13J

m=6.67*10-27kg

Taking proportionality constant 1, the given function will be exponential decaying with

P(0fm)=1

P(5fm)=2.78*10-9

The plot of relative probability is given below

1. A beam of protons of energy 3.75 MeV is incident on a barrier
of height 18.00 MeV and
thickness 1.65 fm (1.65 x 10^ -15 m). (a) What is the probability
of the protons tunneling through the barrier?
(b) By what factor does the probability change if the barrier
thickness is doubled ?

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
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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 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
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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 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
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question if the width is doubled, that is, a = 0.5 nm. (c) Briefly
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When a particle of energy E hits the boundary of a step
potential of potential V0>0 at x=0, when is the probability that
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A.Always
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C.Only if the potential step is positive (that is, V=0 for
x<0, V=V0 for x>0)
D.Only if the potential step is negative (that is, V=V0 for
x<0, V=0 for x>0)
E.Never
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Consider a particle of mass m and energy E approaching the step
potential?
V (x)= 0, x<0
V(x)=V0, x>0
from negative values of x. Consider the case E > V0. a)
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re?ection if E = 2V0?

II(20pts). Short Problems
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