Planck discovered an empirical formula in 1900 that accurately described blackbody radiation spectra across all wavelengths and temperatures. Seeking a physical explanation, he postulated that the walls of a hot cavity contained identical vibrating oscillators that exchange energy with radiation in quantized units proportional to their frequency, called quanta. This quantum hypothesis explained the experimental observations and values Planck calculated for the universal constant h. While initially a mathematical trick, Planck's quantum theory marked a revolutionary beginning of modern quantum mechanics.

1. Planck’s Hypothesis

2. In 1900 Planck 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 lower 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
Thus 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.
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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

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
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