Planck’s hypothesis

1. Planck’s Hypothesis

2. I n 1900 P lanck reported his discovery of a formula that accurately described the shape of a blackbody spectrum for all wavelengths and temperatures. Having found an emperical formula that fit the observations, he then sought a physical reason for the success of the formula.

3. Planck’s thinking began by supposing the existence of identical vibrating oscillators with in the walls of a hot cavity. When a large number of oscillators such as might be found in any ordinary sized object exchange energy radiation is emitted when an oscillator makes a transition from one energy level to a low er one. Absorption of radiation is an inverse process in which the oscillator jumps from a lower energy level to higher one.

4. Planck was forced to assume that the energy of each oscillator was proportional to its frequency. E= hf T hus Planck postulated that vibrational energy is quantized. This is referred to as Planck's quantum hypothesis.

5. Planck himself determined the value of h from previous experimental measurements of blackbody radiation. Planck’s constant is h=6.626×10 J.s.

6. Planck did not draw upon any direct evidence of energy quantization , nor did his results come from extension of the classical theories. Instead he introduced the quantum concept as a modification of classical ideas that brought his theory into agreement with experimental observations. (The word quantum has the same origin as quantity and means the smallest possible unit of energy.)

7. Planck originally suspected that it was a mathematical trick that did not correspond to reality. However, his formula for blackbody radiation commanded attention because of its striking agreement with observations . The replacement of the view that energy flowed like a smooth unbroken stream of water, by one in which energy needed to be thought of as coming in little packets marked the beginning of quantum mechanics and the end in which all physical explanations were in terms of continuous flows or motions.

8. Example: Wavelength of a quantum of radiation. What is the wavelength of a quantum of radiation whose energy is 3.05×10 j? Solution: from the Planck relation, the energy of the radiation is E= hf = hc ƛ The wavelength is obtained from   ƛ= hc = (6.626x10 J.s.)(3.00x m/s) E (3.05x10 J) ƛ=652nm