sciencebriefs
13:00in productionCh. 1 · A barrier too high to climb classically/ 13:00 · ceiling 15 min
Physics

Quantum tunnelling

George Gamow's 1928 theory explained why alpha particles with far too little energy to climb a nucleus's confining wall still escape it, by treating the particle as a wave that can pass through a barrier it cannot classically surmount.

Quantum tunnelling holds that a particle described by a wave function can sometimes pass through an energy barrier that classical physics says it should not have enough energy to cross, because the wave function does not simply stop at the barrier but extends into and, with some probability, through it. George Gamow, working independently alongside Ronald Gurney and Edward Condon, applied this idea in 1928 to solve a specific puzzle in nuclear physics, namely how alpha particles inside a nucleus, carrying only a few million electron volts of energy, manage to escape a confining barrier estimated at around 25 million electron volts high. Their tunnelling-based theory derived mathematically the relationship between decay half-life and emission energy that had previously only been known empirically as the Geiger-Nuttall law, turning an observed pattern into a theoretical result. The same underlying effect later proved essential to explaining nuclear fusion inside stars, and it underlies technologies including the tunnel diode and the scanning tunnelling microscope, which uses a tunnelling current between a sharp tip and a conductive surface to image individual atoms.

Chapters & takeaways6
  1. 0:08
    A barrier too high to climb classically

    Before 1928, physicists could not explain how alpha particles with too little energy to overcome a nucleus's confining barrier still escaped it.

  2. 2:10
    Gamow's tunnelling solution

    George Gamow, alongside Ronald Gurney and Edward Condon, showed in 1928 that treating the particle as a wave let it pass through the barrier rather than over it.

  3. 4:20
    Turning an empirical rule into a derived one

    Their theory mathematically derived the previously empirical Geiger-Nuttall law linking decay half-life to emission energy.

  4. 6:30
    The same effect in stellar cores

    Quantum tunnelling later proved essential to explaining how nuclear fusion occurs in stars despite core temperatures too low to overcome the relevant energy barrier classically.

  5. 8:40
    From theory to the tunnel diode

    Leo Esaki's 1957 demonstration of electron tunnelling across nanometre-scale barriers in semiconductors led to the tunnel diode.

  6. 10:50
    Imaging individual atoms

    Gerd Binnig and Heinrich Rohrer's 1981 scanning tunnelling microscope used tunnelling current to image surfaces at the scale of individual atoms.

Worth your time?

Yes. Study the whole thing.

4.5/ 5
What works
  • states the specific energy mismatch that made alpha decay a genuine puzzle before 1928
  • shows the theory doing real explanatory work by deriving a previously only empirical law
  • connects the same underlying mechanism to genuinely different domains, from stellar fusion to microscopy
What does not
  • does not make tunnelling probability intuitive, since it remains a genuinely non-classical effect
  • cannot be reduced to a single simple mental picture without the underlying wave mathematics
Study it if
  • readers who want the actual physics behind a famously counterintuitive phenomenon
  • anyone curious how a nuclear physics puzzle became a general-purpose theoretical tool
  • people interested in how one effect explains things as different as radioactive decay and atomic-resolution microscopy
Skip it if
  • readers wanting a purely qualitative account without any of the actual energy figures involved
The written brief3 min read

A barrier too high to climb classically

The puzzle this theory solves is a specific mismatch between energy and confinement. Inside certain atomic nuclei, an alpha particle, a tightly bound cluster of two protons and two neutrons, carries only around four to nine million electron volts of energy, yet it sits behind a confining energy barrier estimated at roughly twenty-five million electron volts high. Under classical physics, a particle simply does not have enough energy to climb over a barrier that much higher than its own energy, and yet alpha particles clearly do escape such nuclei on a regular and measurable basis, since alpha decay is a well-documented radioactive process.

Gamow’s tunnelling solution

George Gamow, working independently but at essentially the same time as Ronald Gurney and Edward Condon, resolved this in 1928 by applying quantum mechanics rather than classical mechanics to the problem. Because a particle in quantum theory is described by a wave function rather than a definite trajectory, and that wave function does not abruptly vanish at the edge of a barrier but instead decays gradually within it, there is a small but genuinely nonzero probability that the wave function extends out the other side, meaning the particle can, in effect, pass through the barrier rather than over it. Gurney and Condon described the effect vividly, noting that the alpha particle almost slips away unnoticed.

Turning an empirical rule into a derived one

What made this more than a plausible-sounding story was that Gamow’s mathematical treatment produced a specific, checkable prediction: a relationship between a radioactive nucleus’s half-life and the energy of the alpha particle it emits. This relationship had previously been known only as an empirical pattern, the Geiger-Nuttall law, observed in decay data without a theoretical derivation behind it. Gamow’s tunnelling theory derived that same relationship from first principles, showing that the empirical law was exactly what quantum tunnelling should produce, a strong form of confirmation because the theory was not fitted to the pattern after the fact but reproduced it from independent physical reasoning.

The same effect in stellar cores

The same underlying mechanism turned out to be essential far beyond alpha decay. Inside the core of a star, temperatures are high but still not high enough, by classical reasoning alone, to let positively charged nuclei overcome their mutual electrical repulsion and fuse together at the rate observed. Quantum tunnelling increases the probability that nuclei can penetrate this repulsive barrier despite lacking the classically required energy, and because a stellar core contains an enormous number of nuclei, even a very low tunnelling probability per attempt is enough to sustain the steady, ongoing fusion reactions that power stars including the sun.

From theory to the tunnel diode

The effect also proved technologically useful once physicists learned to engineer it deliberately in solid-state devices. Leo Esaki demonstrated in 1957 that electrons could tunnel across nanometre-scale barriers in semiconductor structures, leading to the development of the tunnel diode, an early practical electronic application of the effect. Related work by Ivar Giaever on tunnelling in superconductors and Brian Josephson’s prediction of tunnelling between superconductors joined Esaki’s work in earning the shared 1973 Nobel Prize in Physics, reflecting how significant controlled electron tunnelling had become for both fundamental physics and electronics.

Imaging individual atoms

Perhaps the most visually striking application came in 1981, when Gerd Binnig and Heinrich Rohrer built the scanning tunnelling microscope, which measures the tiny electric current that tunnels between a very sharp conductive tip and a conductive surface as the tip is scanned across it at a near-atomic distance. Because this tunnelling current depends extremely sensitively on the tip’s distance from the surface, the instrument can resolve individual atoms, a capability that earned Binnig and Rohrer the 1986 Nobel Prize in Physics. From a nuclear physics puzzle in 1928 to imaging individual atoms decades later, this is a rare case of one abstract quantum idea doing genuinely load-bearing explanatory and technological work across entirely different fields.

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