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
ELASTIC COLLISION:  "The collision in which both linear momentum and K.E are conserved is said to be elastic collision".                  OR "In the ideal case when no K

What is a starry sky? Probably one of the most beautiful lighting effects which can be created that can be very simple or rather sophisticated. In its simplest form, a starry s

A step-up transformer works on 220V and gives 2A to an external resistor. The turn ratio between the secondary and primary coils is 2 : 25. Assuming 100% efficiency, Determine the

What is the luminous flux of a flashlight that provides an luminance of 145 lx to the surface of water when held 0.50 m above the water?

Explain how suppressor grid eliminates effect of secondary emission in pentode Ans: Suppressor grid is placed in between plate and screen grid. It's connected with the cathode

Can you put any amount of light into a fiber optic? It is one of the standard fallacies of the industry. The system required to put a sizeable amount of light in a fiber optic

A step-up transformer has a primary coil having of 152 turns and a secondary coil with 3040 turns. The primary coil receives a peak voltage of 98 V. a. What is the effectiv

Define the Working of Spring Cylinder? One part of a cylinder is filled by one mole of a monatomic ideal gas at a pressure of 1 atm and temperature of 300 K. A massless piston


Q. A beam of electrons travelling with a speed of 4 X 10 7 ms -1 is projected normal to a magnetic field of B = 10 -3 Wb m -2 . What is the path of the beam in the magnetic fiel