Quantum_ Einstein, Bohr and the Great Debate About the Nature of Reality - Manjit Kumar [61]
In 1897 the Dutch physicist Pieter Zeeman discovered that in a magnetic field, a single spectral line split into a number of separate lines or components. This was called the Zeeman effect, and once the magnetic field was switched off, the splitting disappeared. Then in 1913 the German physicist Johannes Stark found that a single spectral line splits up into several lines when atoms are placed in an electric field.50 Rutherford contacted Bohr as Stark published his findings: 'I think it is rather up to you at the present time to write something on the Zeeman and electric effects, if it is possible to reconcile them with your theory.'51
Rutherford was not the first to ask. Soon after the publication of Part I of his trilogy, Bohr had received a letter of congratulation from Sommerfeld. 'Will you also apply your atomic model to the Zeeman effect?' he asked. 'I want to tackle this.'52 Bohr was unable to explain it, but Sommerfeld did. His solution was ingenious. Earlier he had opted for elliptical orbits and thereby increased the number of possible quantised orbits that an electron could occupy when an atom was in a given energy state, such as n=2. Bohr and Sommerfeld had both pictured orbits, whether circular or elliptical, as lying in a plane. As he tried to account for the Zeeman effect, Sommerfeld realised that the orientation of an orbit was the vital missing component. In a magnetic field, an electron can select from more permitted orbits pointing in various directions with respect to the field. Sommerfeld introduced what he called the 'magnetic' quantum number m to quantise the orientation of those orbits. For a given principal quantum number n, m can only have values that range from -n to n.53 If n=2, then m has the values: -2, -1, 0, 1, 2.
'I do not believe ever to have read anything with more joy than your beautiful work', Bohr wrote to Sommerfeld in March 1916. The orientation of electron orbits, or 'space quantisation' as it became known, was experimentally confirmed five years later in 1921. It made available extra energy states, now labelled by the three quantum numbers n, k and m, which an electron could occupy in the presence of an external magnetic field, leading to the Zeeman effect.
Necessity being the mother of invention, Sommerfeld had been forced to introduce his two new quantum numbers k and m to explain facts revealed by experiments. Leaning heavily on the work of Sommerfeld, others explained the Stark effect as resulting from the changes in the spacing between energy levels due to the presence of an electric field. Although there were still weaknesses, such as the inability to reproduce the relative intensity of the spectral lines, the successes of the Bohr-Sommerfeld atom further enhanced Bohr's reputation and earned him an institute of his own in Copenhagen. He was on his way to becoming, as Sommerfeld called him later, 'the director of atomic physics' through his work and the inspiration he gave others.54
It was a compliment that would have pleased Bohr, who had always wanted to replicate the way in which Rutherford had run his laboratory, and the spirit he had succeeded in creating among all those who worked there. Bohr had learnt more than just physics from his mentor. He saw how Rutherford was able to galvanise a group of young physicists into producing their best. In 1917 Bohr set out to replicate what he had been fortunate enough to experience in Manchester. He approached the authorities in Copenhagen about establishing an institute for theoretical physics at the university. The institute was approved, as friends raised the money necessary for buildings and