# 7.6 The quantum tunneling of particles through potential barriers  (Page 10/22)

 Page 10 / 22

## Conceptual questions

When an electron and a proton of the same kinetic energy encounter a potential barrier of the same height and width, which one of them will tunnel through the barrier more easily? Why?

What decreases the tunneling probability most: doubling the barrier width or halving the kinetic energy of the incident particle?

doubling the barrier width

Explain the difference between a box-potential and a potential of a quantum dot.

Can a quantum particle ‘escape’ from an infinite potential well like that in a box? Why? Why not?

No, the restoring force on the particle at the walls of an infinite square well is infinity.

A tunnel diode and a resonant-tunneling diode both utilize the same physics principle of quantum tunneling. In what important way are they different?

## Problems

A complex function of the form, $A{e}^{i\varphi }$ , satisfies Schrӧdinger’s time-independent equation. The operators for kinetic and total energy are linear, so any linear combination of such wave functions is also a valid solution to Schrӧdinger’s equation. Therefore, we conclude that [link] satisfies [link] , and [link] satisfies [link] .

A 6.0-eV electron impacts on a barrier with height 11.0 eV. Find the probability of the electron to tunnel through the barrier if the barrier width is (a) 0.80 nm and (b) 0.40 nm.

A 5.0-eV electron impacts on a barrier of with 0.60 nm. Find the probability of the electron to tunnel through the barrier if the barrier height is (a) 7.0 eV; (b) 9.0 eV; and (c) 13.0 eV.

a. 4.21%; b. 0.84%; c. 0.06%

A 12.0-eV electron encounters a barrier of height 15.0 eV. If the probability of the electron tunneling through the barrier is 2.5 %, find its width.

A quantum particle with initial kinetic energy 32.0 eV encounters a square barrier with height 41.0 eV and width 0.25 nm. Find probability that the particle tunnels through this barrier if the particle is (a) an electron and, (b) a proton.

a. 0.13%; b. close to 0%

A simple model of a radioactive nuclear decay assumes that $\text{α}$ -particles are trapped inside a well of nuclear potential that walls are the barriers of a finite width 2.0 fm and height 30.0 MeV. Find the tunneling probability across the potential barrier of the wall for $\text{α}$ -particles having kinetic energy (a) 29.0 MeV and (b) 20.0 MeV. The mass of the $\text{α}$ -particle is $m=6.64\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}{10}^{-27}\phantom{\rule{0.2em}{0ex}}\text{kg}$ .

A muon, a quantum particle with a mass approximately 200 times that of an electron, is incident on a potential barrier of height 10.0 eV. The kinetic energy of the impacting muon is 5.5 eV and only about 0.10% of the squared amplitude of its incoming wave function filters through the barrier. What is the barrier’s width?

0.38 nm

A grain of sand with mass 1.0 mg and kinetic energy 1.0 J is incident on a potential energy barrier with height 1.000001 J and width 2500 nm. How many grains of sand have to fall on this barrier before, on the average, one passes through?

Show that if the uncertainty in the position of a particle is on the order of its de Broglie’s wavelength, then the uncertainty in its momentum is on the order of the value of its momentum.

proof

in the wave equation y=Asin(kx-wt+¢) what does k and w stand for.
derivation of lateral shieft
Hi
Hi
hi
ALFRED
how are you?
hi
asif
hi
Imran
I'm fine
ALFRED
total binding energy of ionic crystal at equilibrium is
How does, ray of light coming form focus, behaves in concave mirror after refraction?
Sushant
What is motion
Anything which changes itself with respect to time or surrounding
Sushant
good
Chemist
and what's time? is time everywhere same
Chemist
No
Sushant
how can u say that
Chemist
do u know about black hole
Chemist
Not so more
Sushant
DHEERAJ
Sushant
But ask anything changes itself with respect to time or surrounding A Not any harmful radiation
DHEERAJ
explain cavendish experiment to determine the value of gravitational concept.
For the question about the scuba instructor's head above the pool, how did you arrive at this answer? What is the process?
as a free falling object increases speed what is happening to the acceleration
of course g is constant
Alwielland
acceleration also inc
Usman
which paper will be subjective and which one objective
jay
normal distributiin of errors report
Dennis
normal distribution of errors
Dennis
photo electrons doesn't emmit when electrons are free to move on surface of metal why?
What would be the minimum work function of a metal have to be for visible light(400-700)nm to ejected photoelectrons?
give any fix value to wave length
Rafi
40 cm into change mm
40cm=40.0×10^-2m =400.0×10^-3m =400mm. that cap(^) I have used above is to the power.
Prema
i.e. 10to the power -2 in the first line and 10 to the power -3 in the the second line.
Prema
there is mistake in my first msg correction is 40cm=40.0×10^-2m =400.0×10^-3m =400mm. sorry for the mistake friends.
Prema
40cm=40.0×10^-2m =400.0×10^-3m =400mm.
Prema
this msg is out of mistake. sorry friends​.
Prema
what is physics?
why we have physics
because is the study of mater and natural world
John
because physics is nature. it explains the laws of nature. some laws already discovered. some laws yet to be discovered.
Yoblaze
physics is the study of non living things if we added it with biology it becomes biophysics and bio is the study of living things tell me please what is this?
tahreem
physics is the study of matter,energy and their interactions
Buvanes
all living things are matter
Buvanes
why rolling friction is less than sliding friction
tahreem
thanks buvanas
tahreem
is this a physics forum
explain l-s coupling