Hydrogen Emission Spectrum, Electrons, and Quantized Energy

I understand that the result of the hydrogen emission spectrum experiment was that only certain wavelengths of light were emitted and that led to the conclusion that electrons emit light when they relax and that they absorb light when they get excited. How does that prove that the energy for electrons are quantized?
 

jfizzix

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if an electron in a hydrogen atom can only absorb and release energy in discrete amounts, then whenever you measure the energy of an electron, it can only have one of a specific set of values (not counting an arbitrary zero point).

In short, if the electron has some energy E0, and it's changes in energy only come from photons with specific allowed frequencies, then the possible values of the energy of that electron will be E0 plus or minus the energies of the photons absorbed and emitted, respectively. We can set E0 to be any number we like, but that won't change the pattern of possible energy values that electron can have, only what counts as "zero".
 

Borek

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What kind of a spectra would you expect to get from an electron if its energy were not quantized? Single lines, or a continuous spectrum?
 
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We would have gotten
A continuous spectrum
If that's the case
The energy of an electron is quantised
Because it can shift from it ground state to its excited one
Only by absorbing discrete or fixed amounts of energy
That's what quantised means
 

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