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The constant was found experimentally when Planck was studying blackbody radiation. He basically found that radiation (eg light) is emitted/absorbed in discrete energy packets (quanta). This is determined by the relationship between the frequency of radiation and Planck's constant. Here's a pretty cool video if you want to learn more about it and how it relates to Quantum Mechanics: https://www.youtube.com/watch?time_cont ... QSbms5MDvY
Planck's constant came about from his studies of black-body radiation. He proposed the exchange of energy between matter and radiation occurs in quanta of energy. You can read more about this in the textbook on page 9-11.
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