The Birth of Planck's Constant

In the late 1900s, a German physicist named Max Planck (1858-1947) had discovered an empirical formula that fit the blackbody spectra, which is…

E = spectral radiance

C1 & C2 = constants

Lambda = wavelength

T = temperature in Kelvin

To evaluate the constants, Planck considered a cavity of temperature filled with blackbody radiation. (Can be thought as a hot oven filled with standing waves of electromagnetic radiation).  Planck attempts to extend the permitted wavelength forever to increasingly shorter wavelengths, such as 2L, L, 2L/3, etc.

 What is Planck’s dilemma if he attempts to extend the wavelengths?

Each permitted wavelength should and could only receive an amount of energy equation to kT, a direct similarity to ideal gas law. This is considered an “ultraviolet catastrophe” because the infinite number of infinitesimally short wavelengths implied that an unlimited amount of blackbody radiation energy was contained in the oven.

Planck attempts to circumvent this problem by using a clever mathematical trick that involves assuming that a standing electromagnetic wave of wavelength and frequency could not acquire just an arbitrary amount of energy, but instead the wave could have only specific energy values that were integral multiples of minimum wave energy, known as quantum of energy.  So given the assumption of quantized wave energy with a minimum energy proportion to the frequency of the wave, the ultraviolet catastrophe can be avoided.

Planck hopes that the constant "h" will be 0, hoping that an artificial constant should not remain as his result.

Planck stratagem worked, but his formula only worked if the constant “h” is a certain value.

Therefore,  the value became known as Planck’s constant, which is 6.26E-34 J/s.