QUANTUM - TUNNELLING

Consider a particle in a one-dimensional box with the walls of finite height and finite thickness,

classically that particle cannot escape from the box unless it's energy is greater than the potential - energy barriers V₀. However, a quantum mechanical treatment which is omitted, shows that there's a finite probability for a particle of total energy lesser than V₀ to be found outside the box.

                                         The term, tunneling is denoted the penetration of a particle into a classically forbidden region.

or passage of particles through a potential - energy barriers whose hight exceeds the particles energy. But since tunneling is a quantum effects, it's probability of occurrences is greater the less classical is the behaviour of the particles. Therefore, tunneling is most prevalent with the particles of little mass. The greater mass m, the more rapidly the functions ψl and ψlll of die away from the zero. 

                Electrons tunnel quite readily, Hydrogen atoms and it's ions tunneling more rapidly than heavier atoms.

                              The emissions of α- particles from a radioactive nucleus involving tunneling of the α-particles through the potential - energy barriers produced by the short-range attractive Coulombic repulsive forces and nuclear forces the daughter nucleus and the α-particles. The ammonia molecule (NH₃) is a pyramidal. There's a potential - energy barriers to inversion of the molecule, with the potential - energy maximum occurs at the planar configuration. The hydrogen atoms can turning through this barrier, thereby inverting the molecule. In CH₃CH₃ there's a barrier to internal rotation, with a potential - energy is maximum at the eclipsed position of the hydrogens. The hydrogen can tunneling through the barriers from one staggered position to the next. Tunneling of electrons is a important in oxidation - reduction reaction and electrode processes. Tunneling usually contributing significantly to the rate of the chemical reaction that involves transferring of hydrogen atoms.

                         Tunneling of Hydrogen atom occurs in some enzymes - catalyzed reactions. The scanning tunneling microscopic, invented in 1981, using the tunneling of electrons through the space between the extremely fine tip of a metal wire and the surface of the electrically conducting solid to procedure image of the individual atoms on the solid's surface. A small voltages is applied between the solid and wire, and as the tip is moving across the surface at a height of a few angstroms, the tip height is adjusted to keeping the current flow constant. A plot of tip height versus position giving image of the surface.