Why do absorptions cause compounds to be coloured.

In summary, the conversation discussed the concept of single wavelength absorptions and their impact on the color of compounds. It was concluded that the visible light spectrum is continuous and composed of many different wavelengths in a range called a "band". The example of copper atoms in solution appearing blue due to absorbing energy in the red spectrum was used to explain how the perception of color is not simply the product of all remaining colors, but can be affected by single wavelength absorptions. The possibility of an infinite number of wavelengths between 400-700 nm was also discussed, along with the role of vibronic coupling in broadening absorption lines. The conversation also touched on the idea that single wavelength absorptions are not the only way photons can interact with matter, and that
  • #1
ampakine
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I don't understand how a handful of single wavelength absorptions could be enough to profoundly alter the colour of the compound. Since the visible light spectrum is continuous doesn't it contain billions of single wavelengths? For example copper atoms in solution appear blue because it absorbs energy in the red spectrum but wouldn't there need to be millions of absorptions in the red spectrum to have an impact on the colour of the light? In other words wouldn't the copper atom need to absorb a band of wavelengths in the red region rather than a handful of specific wavelengths corresponding to the limited number of jumps its d orbital electrons can make?
 
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  • #2
Yes, the colors that are absorbed or reflected are composed of many different wavelengths, all in a range called a "band". The color red is not simply 1 specific wavelength, but many.
 
  • #3
So let's say for example the hydrogen absorption corresponding to a jump from n=1 to n=2. Is it a band of frequencies that gets absorbed there? I thought it was only a single frequency corresponding to the exact energy difference between n=1 and n=2 that gets absorbed. A band being a range of frequencies would be a range of energies.

EDIT: Ah wait, I just read there that if you remove a single wavelength from white light that the eye will perceive the light as the missing wavelengths complementary colour. If that's true that would explain how single wavelength absorptions cause such profound colour changes. I was thinking of it as the perceived colour being the product of all the remaining colours kinda like mixing paint together. I also read that if you combine two single complementary wavelengths of light your eye will perceive it as white light because there are no missing complementary wavelengths. I'm a bit skeptical about that but if that's true that is extremely interesting and I bet there's a mathematical relationship between one wavelength and its complementary wavelength.
 
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  • #4
Also remember that there isn't just 1 state to jump to. The electron could jump from n=1 to n = 100 or whatever. As long as it doesn't get enough energy to be ionized from the atom that is.
 
  • #5
Drakkith said:
Also remember that there isn't just 1 state to jump to. The electron could jump from n=1 to n = 100 or whatever. As long as it doesn't get enough energy to be ionized from the atom that is.

Yeah but the energy difference between n=1 to n=100 would be very different to the difference between 1 and 2 so the absorption would appear at a different area of the spectrum. I can't remember the Rydberg formula off hand but I remember seeing that the energy differences get smaller and smaller the further you move away from the nucleus so there would be much smaller energy difference between 99 and 100 then wouldn't there. Theres something really boggling my mind now. On a continuous spectrum like that what is a unit? Whats a single wavelength? The range between 400 and 700 nm is also the range 400 x 10googleplex and 700 x 10googleplex nm-googleplex. If an absorption corresponds to a single wavelength what is the exact wavelength that gets absorbed?
 
  • #6
Theres something really boggling my mind now. On a continuous spectrum like that what is a unit? Whats a single wavelength? The range between 400 and 700 nm is also the range 400 x 10googleplex and 700 x 10googleplex nm-googleplex. If an absorption corresponds to a single wavelength what is the exact wavelength that gets absorbed?

I can't answer that as I don't know. I don't know if there are actually infinite wavelengths between 400-700 nm or not.

Also, I don't think that absorbtion leading to electrons jumping orbitals is the ONLY way a photon can interact with matter, but I'm not sure.
 
  • #7
Drakkith said:
I can't answer that as I don't know. I don't know if there are actually infinite wavelengths between 400-700 nm or not.

Also, I don't think that absorbtion leading to electrons jumping orbitals is the ONLY way a photon can interact with matter, but I'm not sure.

Yeah I think that's an unanswerable question like "whats the largest number". If laser beams truly are monochromatic then there must be something other than electron jumps going on if they can burn matter.
 
  • #8
ampakine said:
Yeah I think that's an unanswerable question like "whats the largest number". If laser beams truly are monochromatic then there must be something other than electron jumps going on if they can burn matter.

Lasers aren't all exactly 1 wavelength, but a small band.
For example, the following is from wikipedia on lasers.

Most so-called "single wavelength" lasers actually produce radiation in several modes having slightly different frequencies (wavelengths), often not in a single polarization. And although temporal coherence implies monochromaticity, there are even lasers that emit a broad spectrum of light, or emit different wavelengths of light simultaneously.
 
  • #9
ampakine said:
So let's say for example the hydrogen absorption corresponding to a jump from n=1 to n=2. Is it a band of frequencies that gets absorbed there? I thought it was only a single frequency corresponding to the exact energy difference between n=1 and n=2 that gets absorbed. A band being a range of frequencies would be a range of energies.

You are right that absorption in only a single infinitely narrow line would not produce a change of perceived color, as the intensity of the light in that small spectral range would tend to 0. But in the case of dissolved molecules and ions the lines become broad bands due to the coupling of the electronic transitions to all kinds of molecular vibrations (so called vibronic coupling). For each vibrational state, the absorption wavelength occurs at a slightly different frequency and, as the whole system is quantum mechanically, a single molecule can nevertheless potentially absorb at different frequencies at the same time.
 
  • #10
It makes so much sense now!
 
  • #11
ampakine said:
So let's say for example the hydrogen absorption corresponding to a jump from n=1 to n=2. Is it a band of frequencies that gets absorbed there? I thought it was only a single frequency corresponding to the exact energy difference between n=1 and n=2 that gets absorbed. A band being a range of frequencies would be a range of energies.

Atoms are moving, Doppler effect makes this single frequency a band. A narrow one, nonetheless a band.
 
  • #12
Drakkith said:
Also, I don't think that absorbtion leading to electrons jumping orbitals is the ONLY way a photon can interact with matter, but I'm not sure.

Absorption "leading to electrons jumping orbitals" certainly isn't the ONLY way a photon can interact with matter.

A photon is an EM wave "packet" with some known frequency, and the electric field in the EM wave can accelerate electrons in a material (bound to nuclei, or in a "free electron gas" as in a metal) in some oscillatory manner.

Now recall: electrons accelerating (and decelerating) emit EM radiation / photons. If the oscillation is relatively uninhibited, we can get out the same photon energy (explaining reflection or refraction for instance -- although also note there are restrictions about EM waves at boundaries here using Maxwell's equations -- some math we won't get into here). But more interesting: if the electrons are at a surface or boundary, that oscillation can become nonlinear (making solving Maxwell's equations simultaneously at a boundary really fun!)... thus: nonlinear optical materials -- which can be engineered to create some of those two-or-more tone "lasers" -- which we preferred to called optical parametric oscillators in our research).

There's also generally some loss of the initial energy to heating (kinetic motion of the electrons, which can be transferred to other masses within the material). This is why cooler bodies, where the energy has been dispersed to a lower energy/particle level, emit lower energy (more red) photons, and fewer of them overall.

Probably too much info, but fun to think about.
 
  • #13
Thx PG!
 
  • #14
We can be more quantitative: The absorption at a given frequency f is given by Lamberts Beers law:
[tex]
\log{I/I_0}(f)=\epsilon_b(f)lc[/tex]
Here l is the length of the path in the medium, c the concentration of absorbing molecules (or atoms) and [tex]\epsilon_b(f)[/tex] is the molar extinction coefficient which I assume to depend parametrically on some line broadening mechanism b.

The integral [tex] \int df \epsilon_b(f) [/tex] is approximately constant over the line and independent of b.
Then the perceived color will be somehow proportional to
[tex] \int I df/\int I_0 df=\int_{f_0}^{f_0+\Delta f} I_0(f) \exp{\epsilon_b(f)lc}/ \int I_0(f) df [/tex]
If the line is not too broad I_0 is approximately constant for white light and we can use a saddle point approximation for the integral
[tex] \int I_0(f) \exp{(\epsilon_b(f)lc)}/ \int I_0(f) df \approx \exp{(\epsilon_b(f_{max}}lc)} 1/[{\Delta f \cdot \sqrt{2\pi \epsilon_b''(f_{max})}}}][/tex],
The second derivative of the extinction coefficient being inversely proportional to the square of the linewidth. So the perceived color change is approximately proportional to the linewidth.
 
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  • #15
I feel like Peter Griffin when he has to hire a team of engineers and scientists to crunch these massive numbers for him about something simple.:biggrin:
 

1. Why do some compounds appear colored while others are colorless?

The color of a compound is dependent on its molecular structure and the arrangement of its atoms. Specifically, it is the presence of certain chemical bonds and functional groups that allow for the absorption of specific wavelengths of light. Compounds that are colorless do not have these structural features and therefore do not absorb light in the visible spectrum, resulting in no color being observed.

2. How does absorption of light lead to color in compounds?

When a compound absorbs light, it promotes electrons from their ground state to an excited state. The energy of this absorbed light depends on the electrons' energy levels, which are in turn dependent on the structural features of the compound. The absorbed light is then re-emitted, or reflected, at specific wavelengths, giving the compound its characteristic color.

3. Why do some compounds appear different colors in different solvents?

The polarity of a solvent can affect the arrangement and distribution of atoms and bonds in a compound. This can alter the energy levels of the electrons and therefore change the wavelength of light that is absorbed and re-emitted. As a result, a compound may appear different colors in different solvents due to the changes in its electronic structure.

4. Can the color of a compound be predicted based on its molecular structure?

While there are some general trends in color based on the types of chemical bonds and functional groups present in a compound, the color of a specific compound cannot be predicted with complete accuracy. This is because the exact arrangement and distribution of atoms can also have an impact on the compound's color. In addition, factors such as solvent and concentration can also affect the observed color.

5. How do chemists use the color of a compound in their research?

The color of a compound can provide valuable information about its structure, properties, and reactivity. Chemists can use this information to identify and characterize compounds, determine the purity of a sample, and study the mechanisms of chemical reactions. In addition, the color of a compound can also be used in analytical techniques, such as spectrophotometry, to quantitatively measure the concentration of a compound in a solution.

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