1 nanometer ( nm ) = 10 to the -9 meters

1 Angstron ( A ) = 10 to the -10 meters

h = Plancks Constant = 6.625 times 10 to the -27 ers - seconds

f = hertz = frequency ( HZ )

lambda = wavelength at room temperature, at one atmosphere

f = 1 / lambda

E = 1.24 nanometers / lambda

E = H F

http://www.unitconversion.org/unit_converter/energy.html

frequency is cycles per second

joules is the amount of energy or enthalpy per mole

there is a variable missing in your calculation .

that variable is the conversion factor between amount of energy

and cycles per second to go from energy to frequency

Einstein won a Nobel prize for pointing out the evidence that demands quantized energy. Check his bio.

the spectra are composed of discrete lines: particular freqencies.
Why do you think that is?

I understand that the colours represent different frequencies. That when refracted they separate based on the wavelength of the light. Different elements give off unique spectascope signatures... but I am not sure how that ties into the energy being quantized.

Perhaps I am having trouble with the definition of quantized energy. Quanta are the packets of radient energy emitted.
The quantum of enery is ....value, amount of energy?
and quantized energy is the actual wavelength?

Am I on the right track?

yeah well someone decided that the frequency of light (f, measured in hertz) was directly proportional to the amount of energy (E, measured in joules) that each photon has:

E = hf

(the "h" is Plank's constant. So maybe it was him dreamt this up. :)

You getting any closer yet...?

The quantisation idea first came about when plank was trying to explain the emission spectrum of black body radiation, so just google black body radiation and you should find out what you need.

here's a pdf on black body radiation, the more you get into it, the more mathamatical it gets.

[url]http://www.physics.usyd.edu.au/ugrad/jphys/jphys_webct/1902_qm/1902_quantum_notes01.pdf#search='black%20body%20radiation%20AND%20quantisation'[/url]