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  • Define and discuss tunneling.
  • Define potential barrier.
  • Explain quantum tunneling.

Protons and neutrons are bound inside nuclei, that means energy must be supplied to break them away. The situation is analogous to a marble in a bowl that can roll around but lacks the energy to get over the rim. It is bound inside the bowl (see [link] ). If the marble could get over the rim, it would gain kinetic energy by rolling down outside. However classically, if the marble does not have enough kinetic energy to get over the rim, it remains forever trapped in its well.

The figure shows a marble rolling in a semicircular bowl at the top of a volcano. A dashed line is shown just below the top of the bowl indicating maximum distance the marble can travel. A tunnel is shown on one side of the top of the volcano through which the marble can roll downhill.
The marble in this semicircular bowl at the top of a volcano has enough kinetic energy to get to the altitude of the dashed line, but not enough to get over the rim, so that it is trapped forever. If it could find a tunnel through the barrier, it would escape, roll downhill, and gain kinetic energy.

In a nucleus, the attractive nuclear potential is analogous to the bowl at the top of a volcano (where the “volcano” refers only to the shape). Protons and neutrons have kinetic energy, but it is about 8 MeV less than that needed to get out (see [link] ). That is, they are bound by an average of 8 MeV per nucleon. The slope of the hill outside the bowl is analogous to the repulsive Coulomb potential for a nucleus, such as for an α particle outside a positive nucleus. In α decay, two protons and two neutrons spontaneously break away as a 4 He size 12{"" lSup { size 8{4} } "He"} {} unit. Yet the protons and neutrons do not have enough kinetic energy to get over the rim. So how does the α size 12{α} {} particle get out?

The image shows potential energy curve. The curve starts from negative Y axis to positive Y axis and alpha particles are shown trapped inside the nucleus due to attractive nuclear force. The alpha particles outside the range of nuclear force experience the repulsive Coulomb force which keeps them outside the nucleus.
Nucleons within an atomic nucleus are bound or trapped by the attractive nuclear force, as shown in this simplified potential energy curve. An α size 12{α} {} particle outside the range of the nuclear force feels the repulsive Coulomb force. The α size 12{α} {} particle inside the nucleus does not have enough kinetic energy to get over the rim, yet it does manage to get out by quantum mechanical tunneling.

The answer was supplied in 1928 by the Russian physicist George Gamow (1904–1968). The α size 12{α} {} particle tunnels through a region of space it is forbidden to be in, and it comes out of the side of the nucleus. Like an electron making a transition between orbits around an atom, it travels from one point to another without ever having been in between. [link] indicates how this works. The wave function of a quantum mechanical particle varies smoothly, going from within an atomic nucleus (on one side of a potential energy barrier) to outside the nucleus (on the other side of the potential energy barrier). Inside the barrier, the wave function does not become zero but decreases exponentially, and we do not observe the particle inside the barrier. The probability of finding a particle is related to the square of its wave function, and so there is a small probability of finding the particle outside the barrier, which implies that the particle can tunnel through the barrier. This process is called barrier penetration    or quantum mechanical tunneling    . This concept was developed in theory by J. Robert Oppenheimer (who led the development of the first nuclear bombs during World War II) and was used by Gamow and others to describe α size 12{α} {} decay.

Questions & Answers

what is monopoli power
Adzaho Reply
the situation that prevails when economic forces balance so that economic variables neither increase nor decrease
Bombey
what is equilibrium
Kabir
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salihu Reply
Economics is important because it helps people understand how a variety of factors work with and against each other to control how resources such as labor and capital get used, and how inflation, supply, demand, interest rates and other factors determine how much you pay for goods and services.
Muhammad
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Isaac Reply
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Afran
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Humaira
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scor
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scor
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Humaira
the proces of using the services of labor and equipmnt together with other in puts to make goods and services availble
Bombey
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scor
Discuss the short-term and long-term balance positions of the firm in the monopoly market?
Rabindranath Reply
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Mitiku
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Liaqat
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Anteyi Reply
A firm is a business entity which engages in the production of goods and aimed at making profit.
Avuwada
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Avuwada
what is choice
Tia Reply
So how is the perfect competition different from others
Rev Reply
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Tia
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Alfred Reply
1
Naziru
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Anna
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Ukpen
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Docky
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Docky
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Anna
The short run is a period of time in which the quantity of at least one inputs is fixed...
Anna
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Anna
Elacisity
salihu
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Suraj Reply
It will creates rooms for an effective demands.
Chinedum Reply
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babsnof
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Suraj
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eshita
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Suraj
Economics is a science which study human behavior as a relationship between ends and scarce means which has an alternative use.
Mr
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babsnof
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Debless Reply
Demand refers to the quantity of products that consumers are willing to purchase at various prices per time while Supply has to do with the quantity of products suppliers are willing to supply at various prices per time. find the difference in between
Saye
what is demand
Humaira
demand is a relationship btn the price of an item and the quantity demanded
Bombey
Difference between extinct and extici spicies
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Source:  OpenStax, College physics -- hlca 1104. OpenStax CNX. May 18, 2013 Download for free at http://legacy.cnx.org/content/col11525/1.1
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