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The phenomenon of tunneling, which has no counterpart in classical physics, is an important consequence of quantum mechanics. Consider a particle with energy E in the inner region of a one-dimensional potential well V(x), as shown. (A potential well is a potential that has a lower value in a certain region of space than in the neighbouring regions.) In classical mechanics, if E < V0 (the maximum height of the potential barrier), the particle remains in the well forever; if E > V0, the particle escapes. In quantum mechanics, the situation is not so simple. The particle can escape even if its energy E is below the height of the barrier V0, although the probability of escape is small unless E is close to V0. In that case, the particle may tunnel through the potential barrier and emerge with the same energy E.
The phenomenon of tunneling has many important applications. For example, it describes a type of radioactive decay in which a nucleus emits an alpha particle (a helium nucleus). According to the quantum explanation given independently by George Gamow and by Ronald W. Gurney and Edward Condon in 1928, the alpha particle is confined before the decay by a potential of the shape shown in Figure 1. For a given nuclear species, it is possible to measure the energy E of the emitted alpha particle and the average lifetime τ of the nucleus before decay. The lifetime of the nucleus is a measure of the probability of tunneling through the barrier—the shorter the lifetime, the higher the probability. With plausible assumptions about the general form of the potential function, it is possible to calculate a relationship between τ and E that is applicable to all alpha emitters. This theory, which is borne out by experiment, shows that the probability of tunneling, and hence the value of τ, is extremely sensitive to the value of E. For all known alpha-particle emitters, the value of E varies from about 2 to 8 million electron volts, or MeV (1 MeV = 106 electron volts). Thus, the value of E varies only by a factor of 4, whereas the range of τ is from about 1011 years down to about 10−6 second, a factor of 1024. It would be difficult to account for this sensitivity of τ to the value of E by any theory other than quantum mechanical tunneling.

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FAQs on Tunneling, Basic Concepts and Methods - Modern Physics for IIT JAM

1. What is tunneling in physics?
Ans. Tunneling in physics refers to the phenomenon where a particle passes through a potential barrier that it classically cannot overcome. It is a quantum mechanical effect that occurs due to the wave-like nature of particles. The particle has a non-zero probability of penetrating the barrier and appearing on the other side, even though it does not have enough energy to surmount the barrier according to classical physics.
2. How does tunneling occur?
Ans. Tunneling occurs when a particle encounters a potential energy barrier. According to quantum mechanics, particles can be described as waves, and these waves can extend beyond the region where the particle's energy is classically allowed. When a particle wave encounters a barrier, there is a probability that it will "tunnel" through the barrier and continue propagating on the other side. This probability is determined by the wavefunction of the particle and the characteristics of the barrier.
3. What are the applications of tunneling in physics?
Ans. Tunneling has various applications in physics. It is widely used in scanning tunneling microscopy (STM), where a sharp tip is brought very close to a surface, allowing electrons to tunnel between the tip and the surface. This technique provides atomic-scale resolution and has been used to study surface structures and manipulate individual atoms. Tunneling is also essential in tunnel diodes, which are electronic devices used in high-speed electronics and telecommunications.
4. Can tunneling occur with macroscopic objects?
Ans. Tunneling is primarily observed at the microscopic scale, involving particles such as electrons or atoms. According to current understanding, it is highly unlikely for macroscopic objects, such as everyday objects or living organisms, to tunnel through macroscopic barriers. The energy required for a macroscopic object to tunnel through a macroscopic barrier would be astronomically large, making it effectively impossible.
5. How does tunneling relate to nuclear fusion?
Ans. Tunneling plays a crucial role in nuclear fusion, the process that powers the Sun and other stars. In the Sun's core, atomic nuclei overcome the electrostatic repulsion between them and fuse together to release energy. Quantum tunneling allows these nuclei to overcome the Coulomb barrier, which is the energy barrier resulting from their positive charges. Without tunneling, nuclear fusion would be significantly hindered, and the Sun would not be able to sustain its energy production.
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