[Il Divo]

So maybe I'm approaching this from the wrong angle, but

according to Planck, energy is quantized, according to the equation E = hν. Once a frequency for electromagnetic radiation has been established, total energy can only exist in whole number multiples of the above equation.

How is white light, representing a continuous spread of wavelengths and also energies (since c = λν), possible if energy is said to exist in discrete quantities? This appears to be in contrast to the emission spectra of specific elements such as Hydrogen and Helium which clearly demonstrate a discrete spread of colors, due to the fact that they have very specific energy level separations. 

As a side note, why are solids special in their ability to emit all wavelengths, in comparison to the gas phase spectra of elements?

Apologies if I'm confusing something critical or basic.

[Borek]

You are making a common mistake. Energy is quantized for a given system, not in general terms. By system I mean something like an atom, or a molecule etc. As there are infinitely many possible systems, you can always find one for which given quant is the correct one.

[Il Divo]

You are making a common mistake. Energy is quantized for a given system, not in general terms. By system I mean something like an atom, or a molecule etc. As there are infinitely many possible systems, you can always find one for which given quant is the correct one.

So is energy only quantized in the sense that once we specify a frequency, the values of energy are then restricted according to Planck's equation?

Or to put it another way: quanta/photons are restricted to integer values, but what constitutes a quanta of energy has infinite possibilities?

[Borek]

So is energy only quantized in the sense that once we specify a frequency, the values of energy are then restricted according to Planck's equation?

There is ONE energy for a given frequency.

Or to put it another way: quanta/photons are restricted to integer values, but what constitutes a quanta of energy has infinite possibilities?

For a given system energy is a multiply of some value, but not necessarily each integer multiply. For example in quantum physics energy of a rigid rotor (something like an idealized dumbbell with point masses) is

[tex]E_\ell=\frac {\hbar^2}{2I} \ell(\ell+1)[/tex]

(where I is a moment of inertia of the rotor) and [itex]\ell[/itex] is a natural number (including zero). That means possible values of energy are 0 (for [itex]\ell=0[/itex]), [itex]\frac {2\hbar^2}{2I}[/itex] (for [itex]\ell=1[/itex]), [itex]\frac {6\hbar^2}{2I}[/itex] (for [itex]\ell=2[/itex]), but never [itex]\frac {3\hbar^2}{2I}[/itex] or [itex]\frac {4\hbar^2}{2I}[/itex].

Note, that changing I (that is, changing masses of the rotor, or distance between them) you can construct a rotor that will take any energy you want.

[Arkcon]

Working with your initial premise, how white light exists given quantized energy:  an individual photon has a quantized energy, and associated frequency.  It can fly through space, situated next to several other photons, each with their own quantized energy.  The interactions of white light with matter, say of a photocell or the human retina, is likewise an average of many individual photon to atom interactions.

[juanrga]

So maybe I'm approaching this from the wrong angle, but

according to Planck, energy is quantized, according to the equation E = hν. Once a frequency for electromagnetic radiation has been established, total energy can only exist in whole number multiples of the above equation.

How is white light, representing a continuous spread of wavelengths and also energies (since c = λν), possible if energy is said to exist in discrete quantities? This appears to be in contrast to the emission spectra of specific elements such as Hydrogen and Helium which clearly demonstrate a discrete spread of colors, due to the fact that they have very specific energy level separations. 

As a side note, why are solids special in their ability to emit all wavelengths, in comparison to the gas phase spectra of elements?

Apologies if I'm confusing something critical or basic.

Light is made of photons, somewhat as matter is made of electrons and quarks. The continuity of matter and light at large scales is only apparent.

If you have molecules in diluted gas phase, each molecule is, at a good approximation, independent of the others. Each molecule, with N electrons, absorbs/emits light according to the available energy levels (roughly there are N spaced levels).

A solid is a giant molecule with many many atoms, which implies many many energy levels, which are so close that look as a continuum. The solid absorbs/emits light according to a quasi continuum of available energy levels

[Il Divo]

Thanks to everyone for the responses! I really appreciate it and think I have a much better understanding of how white light functions.