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How Niels Bohr predicted Rydberg atoms

Saturday, January 27, 2024 7:01

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In Niels Bohr’s original 1913 formulation of the quantum atom, the Bohr radius r was proportional to n^2, n being the principal quantum number. Highly excited states would correspond to very large values of n and Bohr predicted these “giant” atoms would exist. Since the volume scales as r^3 or n^6, for n=33 you should see a “hydrogenic” atom a billion times larger than a ground state hydrogen atom. However, no spectral lines corresponding to such atoms were observed. So was Bohr’s theory wrong?

No! Bohr pointed out that unlike physicists, *astronomers* had observed faint spectral lines in the spectra or stars and nebulae, consistent with his theory. Because of the large proportion of gas and low density, he predicted such highly excited states would exist.

Because of the extremely low densities, these excited states could live for as long as 1 second – a lifetime for an atom. In 1957, astronomers looking for electron-proton recombination in the interstellar medium serendipitously observed spectra from hydrogen atoms for n=110! In the 1970s, after Bohr’s death, the advent of tunable dye lasers finally made it possible to observe these excited states in the lab. Because of their long lifetimes and huge electric dipole moments, these atoms have potential applications in quantum computing.

These “atoms” are called Rydberg atoms because Johannes Rydberg had hypothesized about these large-quantum-number states in the 19th century. But Bohr provided a physical basis and an explanation, so they should really be called Rydberg-Bohr atoms at the least. Today, Rydberg atoms have diverse applications ranging from lasers to quantum computing to plasma physics to radio receivers for military applications. But it all goes back – almost as an afterthought – to Bohr’s original pioneering 1913 paper and should be recognized as such.

Source: http://wavefunction.fieldofscience.com/2024/01/how-niels-bohr-predicted-rydberg-atoms.html

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