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It isn't so much a matter of there being a given "quantum of energy" as much as energy is quantized. This means that particles that behave quantum mechanical laws can only have certain values of energy and not the values in between. The most popular example of this is an electron in an atom. Quantum theory tells us that the electron can be in it's ground state energy, which has a given value, or it's first excited state, which has another given value, or any higher excited state. However, you cannot observe an electron with an energy value in between the ground state and first excited state, or between any two consecutive excited states. This is what it means to have quantized energy: only certain discrete values are allowed.

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