Tunneling and tunneling applications, Physics

Assignment Help:

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.


Related Discussions:- Tunneling and tunneling applications

What is the slit separation, Light with a wavelength of 454.5 nm passes by ...

Light with a wavelength of 454.5 nm passes by two slits that are 95.2 cm from a screen. The distance among the centers of the central band and the first-order band is 15.2 mm.

Speed of light, what will happen if we will walk with the speed of light or...

what will happen if we will walk with the speed of light or faster than it?

Describe critical angle, The measurements taken in Ramdesns eyepiece more w...

The measurements taken in Ramdesns eyepiece more worthy (reliable) than Huygens eyepiece. Why? Describe critical angle. show its relationship with refractive index.

Write the expression for equivalent focal length, What occures to the norma...

What occures to the normal shift when the thickness of the optical medium is decreased? Write down the expression for equivalent focal length of combination of two thin lenses d

Calculate the tangential acceleration, The airplane shown in the figure is ...

The airplane shown in the figure is to achieve "weightlessness" for a short period of time by flying along a curved path such that it's acceleration components in x direction a x

Magnetic lines of flux, Magnetic lines of flux   A line of flux is ...

Magnetic lines of flux   A line of flux is a line indicating the direction in which a free north pole would travel, if placed in the field at that point. Alternatively it

Define peltier coefficient, Q. Define: Peltier coefficient and write its un...

Q. Define: Peltier coefficient and write its unit. The quantity of heat energy absorbed or evolved at one of the junctions of a thermocouple when one ampere current flows for

Mechanical properties of solids, Assignment of applications of elastic beha...

Assignment of applications of elastic behaviour of materials

Can you define solar constant, Q. Can you define Solar Constant? The lu...

Q. Can you define Solar Constant? The luminosity of the Sun L is 3.827×10 26 Watts. When the Sun is straight overhead on a clear day how many watts would we expect to illumina

Write Your Message!

Captcha
Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd