Short answers, pulled from the story.
Max Planck imposed a new boundary condition requiring energy quantization to match observed spectral distribution. He described this solution as an act of desperation and used statistical mechanics to derive his result. His calculated value fell within 1.2% of the currently defined value.
Albert Einstein proposed that light is quantized into small packets called photons with energy proportional to frequency. The constant of proportionality between incident light frequency and photoelectron kinetic energy proved equal to the Planck constant h. This discovery earned him the Nobel Prize in Physics in 1921.
John William Nicholson developed an atomic model in 1912 where electron angular momentum related by h divided by two. Niels Bohr quoted Nicholson in his own 1913 paper about the hydrogen atom. An electron within this Bohr atom could only possess certain defined energies determined by specific equations involving the speed of light and the Rydberg constant.
Werner Heisenberg formulated fundamental limits on measurement precision using the Planck constant to relate position and momentum uncertainties. The inverse relationship forced a tradeoff in quantum experiments where measuring one quantity precisely made the other imprecise. One example involved time versus energy pairs following similar rules.
Louis de Broglie generalized the Planck-Einstein relation in 1923 by postulating that the constant represented proportionality between momentum and quantum wavelength for any particle. This hypothesis extended beyond photons to include all elementary particles like electrons or neutrons. The de Broglie wavelength of a particle equals Planck's constant divided by linear momentum.
Metrologists fixed the exact value of the Planck constant in 2018 to redefine the SI unit of mass during voting at the General Conference on Weights and Measures in Versailles, France. Technologies such as the Kibble balance measured the kilogram by fixing this numerical value when expressed in joule-seconds. The new definition stated the kilogram is determined by taking the fixed numerical value of h to be exactly 6.62607015 times ten to the minus thirty-four joule-seconds.