Photoelectric Effect

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Einstein’s Quanta, Entropy, and the Photoelectric Effect
E LEGANT C ONNECTIONS

IN

P HYSICS

“On

a Heuristic Point of View Concerning the Production and Transformation of
Light”[1] was the first of the five papers published by
Albert Einstein in his 1905 “miraculous year.”[2] In that paper, Einstein introduced the concept of “light quanta,” or “photons” as we call them today.
The quantum of action was introduced into physics by Max Planck in 1900.[3] Planck derived the thermal equilibrium energy distribution for electromagnetic radiation (also called the “blackbody problem” because of the experimental apparatus). The quantity of interest was dr/df where r denotes the energy density and f the frequency (Fig. 1). No one had been able to derive dr/df from the first principles of statistical mechanics. One serious problem was in the high frequencies, which contributed infinite energy when one integrated over all frequencies to obtain the total energy!
Planck thought about the charged particles whose simple harmonic motion generated harmonic electromagnetic waves of the same frequency. He discovered that if he assumed a particle oscillating with frequency f could carry only the discrete energies 0, hf, 2hf, 3hf..., where h was a constant, he could derive the distribution function: dr/df = (8ph/c3) f 3 (e hf/kT − 1)−1 , where c denotes the speed of light in vacuum, k
Boltzmann’s constant, and T the absolute temperature.
This function fit the data provided h was assigned the value 6.6×19−34 J · s, now called Planck’s constant.[4]
The smallness of h accounted for the lack of energy graininess in macroscopic oscillators such as pendulums.
To Planck in 1900, the quantum was a property of the mechanical oscillators that happen to generate light.
Radiation itself, in principle, would still…...

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