Quantum_ Einstein, Bohr and the Great Debate About the Nature of Reality - Manjit Kumar [78]
In 1922, the year Einstein lectured in Paris at the invitation of Langevin and received a hostile reception for having remained in Berlin throughout the war, de Broglie wrote a paper in which he explicitly adopted 'the hypothesis of quanta of light'. He had already accepted the existence of 'atoms of light' at a time when Compton had yet to make any sort of announcement concerning his experiments. By the time the American published his data and analysis of the scattering of X-rays by electrons and thereby confirmed the reality of Einstein's light-quanta, de Broglie had already learned to live with the strange duality of light. Others, however, were only half-joking when they complained about having to teach the wave theory of light on Mondays, Wednesdays and Fridays, and the particle theory on Tuesdays, Thursdays and Saturdays.
'After long reflection in solitude and meditation,' de Broglie wrote later, 'I suddenly had the idea, during the year 1923, that the discovery made by Einstein in 1905 should be generalized by extending it to all material particles and notably to electrons.'12 De Broglie had dared to ask the simple question: if light waves can behave like particles, can particles such as electrons behave like waves? His answer was yes, as de Broglie discovered that if he assigned to an electron a 'fictitious associated wave' with a frequency v and wavelength , he could explain the exact location of the orbits in Bohr's quantum atom. An electron could occupy only those orbits that could accommodate a whole number of wavelengths of its 'fictitious associated wave'.
In 1913, to prevent Rutherford's model of the hydrogen atom from collapsing as its orbiting electron radiated energy and spiralled into the nucleus, Bohr had been forced to impose a condition for which he could offer no other justification: an electron in a stationary orbit around the nucleus did not emit radiation. De Broglie's idea of treating electrons as standing waves was a radical departure from thinking about electrons as particles orbiting an atomic nucleus.
Standing waves can easily be generated in strings tethered at both ends, such as those used in violins and guitars. Plucking such a string produces a variety of standing waves with the defining characteristic that they are made up of a whole number of half-wavelengths. The longest standing wave possible is one with a wavelength twice as long as the string. The next standing wave is made up of two such half-wavelength units, giving a wavelength equal to the physical length of the string. The next is a standing wave consisting of three half-wavelengths, and so on up the scale. This whole number sequence of standing waves is the only one that is physically possible, and each has its own energy. Given the relationship between frequency and wavelength, this is equivalent to the fact that a plucked guitar string can vibrate only at certain frequencies beginning with the fundamental tone, the lowest frequency.
De Broglie realised that this 'whole number' condition restricted the possible electron orbits in the Bohr atom to those with a circumference that permitted the formation of standing waves. These electron standing waves were not bound at either end like those on a musical instrument, but
Figure 9: Standing waves of a string tethered at both ends
were formed because a whole number of half-wavelengths could be fitted into the circumference of the orbit. Where there was no exact fit, there could be no standing wave and therefore no stationary