## Classical to Quantum Mechanics

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#### In order to reproduce the formula which he had empirically derived and presented in October 1900, Planck found that he could only do so if he assumed that the radiation was produced by oscillating electrons, which he modelled as oscillating on a massless spring (so-called “harmonic oscillators”). The total energy at any given frequency would be given by the energy of a single oscillator at that frequency multiplied by the number of oscillators oscillating at that frequency.

However, he had to assume that

1. The energy of each oscillator was not related to either the square of the amplitude of oscillation or the square of the frequency of oscillation (as it would be in classical physics), but rather just to the frequency,
E α ν
2. The energy of each oscillator could only be a multiple of some fundamental “chunk” of radiation, , so En = nhν
where n = 0, 1, 2, 3, 4
3. The number of oscillators with each energy Ewas given by the Boltzmann distribution, so

Nn = N0e–nhν/kT

where N0 is the number of oscillators in the lowest energy state.

By combining these assumptions, Planck was able in November 1900 to reproduce the exact equation which he had derived empirically in October 1900. In doing so he provided, for the first time, a physical explanation for the observed blackbody curve.

7. #### Thus an electromagnetic cycle consists of a pulse of energy of magnitude ‘h’. A three-dimensional electromagnetic field is made up of such dynamic pulses.

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