Quantum_ Einstein, Bohr and the Great Debate About the Nature of Reality - Manjit Kumar [55]
Had Ångström lived (he died in 1874 aged 59), he would have been astounded by Balmer's use of his formula to predict the existence of other series of spectral lines for the hydrogen atom in the infrared and ultraviolet regions by simply setting n to 1, 3, 4 and 5 while letting m cycle through different numbers, as he had done with n set at 2 to generate the four original lines. For example, with n=3 and m=4 or 5 or 6 or 7…, Balmer predicted the series of lines in the infrared that were discovered in 1908 by Friedrich Paschen. Each of the series forecast by Balmer was later discovered, but no one had been able to explain what lay behind the success of his formula. What physical mechanism did the formula, arrived at through a process of trial and error, symbolise?
'As soon as I saw Balmer's formula,' Bohr said later, 'the whole thing was immediately clear to me.'22 It was electrons jumping between different allowed orbits that produced the spectral lines emitted by an atom. If a hydrogen atom in the ground state, n=1, absorbs enough energy, then the electron 'jumps' to a higher-energy orbit such as n=2. The atom is then in an unstable, excited state and quickly returns to the stable ground state when the electron jumps down from n=2 to n=1. It can do so only by emitting a quantum of energy that is equivalent to the difference in energy of the two levels, 10.2eV. The wavelength of the resulting spectral line can be calculated using the Planck-Einstein formula, E=hv, where v is the frequency of the emitted electromagnetic radiation.
An electron jumping from a range of higher energy levels to the same lower energy level produced the four spectral lines of the Balmer series. The size of the quanta emitted depended only on the initial and final energy levels involved. This was why Balmer's formula generated the correct wavelengths when n was set equal to 2 but m was 3, 4, 5 or 6 in turn. Bohr was able to derive the other spectral series predicted by Balmer by fixing the lowest energy level that the electron could jump to. For example, transitions ending with the electron jumping to n=3 produced the Paschen series in the infrared, while those that ended at n=1 generated the so-called Lyman series in the ultraviolet region of the spectrum.23
Figure 7: Energy levels, line spectra and quantum jumps (not drawn to scale)
There is, as Bohr discovered, a very strange feature associated with an electron's quantum leap. It is impossible to say where an electron actually is during a jump. The transition between orbits, energy levels, has to occur instantaneously. Otherwise as the electron travelled from one orbit to another it would radiate energy continuously. In Bohr's atom, an electron could not occupy the space between orbits. As if by magic, it disappeared while in one orbit and instantly reappeared in another.
'I'm fully convinced that the problem of spectral lines is intimately tied to the question of the nature of the quantum.' Remarkably, it was Planck, in February 1908, who wrote these words in a notebook.24 But in his ongoing struggle to minimise the impact of the quantum, and before the Rutherford atom, it was as far as Planck could go. Bohr embraced the idea that electromagnetic radiation was emitted and absorbed by atoms in quanta, but in 1913 he did not accept that electromagnetic radiation itself was quantised. Even six years later, in 1919, few believed in Einstein's quantum of light when Planck declared in his Nobel Prize lecture that Bohr's quantum atom was 'the long-sought key to the