Quantum Tunnelling and the Transmission Probability
A particle meeting a barrier it cannot classically cross has a small chance of appearing on the far side, falling off exponentially with barrier width and height. Alpha decay and the scanning tunnelling microscope both live on that exponential.
What a learner can do afterwards
- Relates transmission probability to barrier width, height and particle mass
- Explains alpha decay as tunnelling out of the nuclear potential
- Says why the tunnelling microscope resolves single atoms
1 · Read
Tunnelling lets a particle cross a barrier it classically cannot climb. The wave fades exponentially inside the wall, yet a small transmitted wave emerges on the far side. The crossing chance drops exponentially with barrier width, height, and the particle mass: thin low barriers leak, while thick high ones barely do. Run the triple test on any barrier question first: wider means weaker, taller means weaker, heavier means weaker.
Alpha decay is tunnelling at work. An alpha particle sits trapped by the nuclear wall without the energy to climb over, yet it escapes by tunnelling out. Because the rate is exponential in width, a slightly thicker wall means a vastly longer half-life, which explains the huge observed range. The same exponential rule governs devices and decays alike.
The scanning tunnelling microscope turns the exponential into vision. Electrons jump a vacuum gap between tip and surface, and the current swings wildly with tip distance, so scanning maps single atoms. Heavier particles tunnel far less readily than electrons under identical barriers, which is why the microscope uses electrons and not ions.
Predict before you compute. Apply the triple test to rank barriers, and remember that a small width change multiplies the rate by orders of magnitude. Total energy stays the same throughout: the particle never owns extra energy inside the wall, it simply appears on the far side with unchanged E.
Tunnelling falls exponentially with width, height, and mass, which explains alpha decay spreads and lets a microscope current feel single atoms.
2 · Watch
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Where it sits
8 questions wait behind this lesson, each with its answer explained. Every answer feeds the sky: stars light as they are learned, and dim when it is time to come back.