Tunneling and tunneling applications, Physics

Q. What is quantum mechanical "Tunneling"? Give one example.

OR

What do you mean by quantum mechanical tunneling? Show that the tunneling probability is given by the expression.

Where U0 =Height of the rectangular potential barrier. Draw graphs showing variation of T with particle energy E and barrier width a.

OR

With help of suitable diagrams explain the phenomenon of quantum mechanical tunneling in a- decay process.

Ans.

Tunnel Effect : Tunnel effect is purely a quantum mechanical phenomenon, absolutely inconceivable in classical physics. The reason is that a particle "in the tunnel" ought to have a negative kinetic energy. In quantum mechanics, the division of the total energy into kinetic and potential energies has no sense because it contradicts the uncertainty principle. If we say that a particle has a definite kinetic energy K it would mean that it has a definite momentum. Similarly, as a particle with a definite location in space. Since the momentum and location of a particle cannot simultaneously have definite values, it is impossible to find simultaneously exact values of kinetic and potential energies. Thus, although the total energy E of a particle has a quite definite value, it cannot be represented in the form of the sum of the exactly determined energies K and V. Hence in quantum mechanics the  conclusion that K is negative inside the tunnel is meaningless.

Application of Tunnel Effect - (Theory of a - decay)

The tunnel effect has been applied to explain the emission of particles from radioactive nuclei. The average energy of an a particle formed within the nucleus is less than the height of the potential barrier around the nucleus which is formed by the nuclear binding forces. Classically, the a-particle cannot escape from the nucleus, but quantum mechanically it "tunnels" through the barrier. This tunneling explains radioactive a decay.

The tunnel effect has also been found responsible for the "field emission" of electrons form metals. This is the emission of electrons by metals in vacuum subjected to strong electric fields. Classically, the field must be much more stronger than the actual fields at which the emission actually occurs. The actual field, however, reduces the width of the barrier for electrons at the metal vacuum interface, so that electrons of energy less than the barrier height can "tunnel" through the barrier.

Posted Date: 7/11/2012 3:04:12 AM | Location : United States







Related Discussions:- Tunneling and tunneling applications, Assignment Help, Ask Question on Tunneling and tunneling applications, Get Answer, Expert's Help, Tunneling and tunneling applications Discussions

Write discussion on Tunneling and tunneling applications
Your posts are moderated
Related Questions
explain quantization of charge

Definition: The electric field in a region is shown by continues lines (also known as lines of force). Field line is an imaginary line along which a positive test charge will move

Constancy principle (A. Einstein): One of the postulates of A. Einstein's special theory of relativity, that puts forth that the speed of light in vacuum is calculated as the

Jonathan, with a mass of 81 kg, starts at rest from the top of a water slide angled at 42° from the ground. He exits at the bottom 3.0 s later going 15 m/s. What is μk?

Simple steelyard (reading to 100 g) The pan is made from cardboard, and is formed like a funnel. It is fixed to a beam made of a triangular-shaped lamina in ply- wood or 'Persp

1 Volt : Potential difference among two points will be 1 volt if 1 joule of work is needed to move a +ve charge of Coulumb from 1 point to another.

(i) A closed system consisting of 2 kg of a gas undergoes a process during which the relationship between pressure and specific volume is pv1.3 = c. The process begins with 1 p =1b

Explain the first law of thermodynamics. Reduce its mathematical form, give the first law equation for different processes. What are its limitations?

What is Centrifugal Force? Centrifugal force is the force that is equivalent in magnitude but opposite in direction to the centripetal force, which is the force directed toward

An organ pipe which is open at both ends resonates at its fundamental frequency. Neglecting any end effects, what wavelength is formed by this pipe in this mode of vibration if the