Question

Your friend has just finished classical physics and can't wait to know what lies ahead. Keeping extraneous ideas and postulates to is minimum. explain the process of quantum-mechanical tunneling.

Short answer

Quantum-mechanical tunneling is a phenomenon in quantum physics where particles can pass through a potential barrier even if their energy is less than the energy of the barrier. The particles are described by wave functions, mathematical expressions that give probability of finding a particle in a certain state. The wave function can extend into regions where, in classical physics, a particle should not be able to reach, giving a non-zero probability that the particle can 'tunnel' through barriers. Examples include radioactive decay and the operation of trunneling microscopes.

Step-by-step solution

Definition

Quantum-mechanical tunneling is a phenomenon in quantum physics where particles can pass through a potential barrier even if their energy is less than the energy of the barrier. This occurs because of the wave nature of particles in quantum mechanics.

Explain Wave Nature of Particles

In quantum physics, particles are described by wave functions, mathematical expressions that give probability of finding a particle in a certain state. According to the principles of quantum mechanics, these wave functions can extend into regions where classically, a particle should not be able to go.

Present Understanding of the Phenomenon

When a particle encounters a barrier, its wave function decreases exponentially within the barrier (assuming its energy is less than the energy of the barrier) but does not go to zero. Hence, there is a non-zero probability that the particle can be found on the other side of the barrier, having 'tunneled' through the barrier.

Give Examples

'Tunneling' is used to explain various physical phenomena, including radioactive decay and the operation of scanning tunneling microscopes. In radioactivity, tunneling can explain how alpha particles escape the nucleus. In scanning tunneling microscopes, a sharp tip is brought close to the surface of a material, and electrons can tunnel between the tip and the surface.

Key concepts

Wave Nature of Particles

In the world of quantum mechanics, particles such as electrons are not just little billiard balls but have a wavy aspect to their nature as well. This is called the 'wave nature of particles'. In classical physics, we usually think of objects as being in a specific place at a specific time. But in quantum mechanics, things get a bit more dreamy.

Particles are described by something known as a wave function. This is a mathematical recipe that tells us the probability of finding a particle in a certain place. It's like the particle is spread out over an area, and the wave function lets us know how likely it is to find it at any given point.

• The wave function can 'leak' into areas where, according to classical physics, the particle shouldn't be found.
• This leakage is what allows for phenomena like quantum tunneling, where particles can seemingly pass through barriers.

Understanding this nature of particles helps explain why they can do the seemingly impossible things they do in quantum mechanics.

Quantum Mechanics

Quantum mechanics is a fundamental theory in physics that provides a description of the physical properties of nature at the smallest scales. It's like having a brand new set of rules that govern tiny particles like electrons, photons, and even atoms.

This theory includes perplexing concepts such as superposition, where particles can exist in multiple states until they're observed, and entanglement, where particles can be interconnected in ways that defy classical logic.

• Quantum mechanics fundamentally changes the way we see the universe.
• It introduces the idea that uncertainty is a basic feature of the atomic and subatomic realm.

Quantum mechanics also provides the framework for understanding quantum-mechanical tunneling, as it's the wave aspect of particles that allows them to tunnel through barriers. This wouldn't make sense in the classical view, but it's everyday physics in the quantum world!

Radioactive Decay

Radioactive decay is a process where unstable atomic nuclei lose energy by emitting radiation. It’s a natural event, kind of like a high-energy version of how an ice cube gradually melts.

In the context of quantum mechanics, a fascinating part of decay is explained by tunneling. For instance, in alpha decay, an alpha particle (which is a type of radiation) can escape the nucleus even though it doesn't have enough energy to overcome the nuclear force keeping it inside, at least not in the way classical physics would assume.

• The wave nature of the alpha particle allows it to have a probability of being beyond the barrier.
• Once it 'tunnels' through, it pops out on the other side and the nucleus decays.

Thus, quantum tunneling provides an elegantly simple explanation for the spontaneous release of particles like alpha particles during radioactive decay.

Scanning Tunneling Microscopes

One of the practical applications of quantum-mechanical tunneling is found in the scanning tunneling microscope (STM). This ingenious device allows us to visualize surfaces at the atomic level!

Imagine an extremely sharp needle tip brought extremely close to a material's surface. The distance is so tiny it's like trying to measure the width of a thin piece of paper — but viewed from outer space.

• Electrons from the material can tunnel across the small gap from the surface to the tip.
• This tunneling creates an electric current that can be measured.

By moving the tip across the surface and measuring the tunneling current, scientists can map out the structure of the surface at an incredibly detailed level. This all revolves around the wave function of electrons, which, thanks to quantum mechanics, allows them to hop through thin barriers, making visualizing individual atoms possible!