Very interesting explanation as to how colour or elements are what they are, least for explaining silver and gold.
Certainly for non oxided elements, Bismuth being a wonderful element colour wise with oxidisation in effect.
I do enjoy articles like this as they explain the more common building blocks of elements in a way that gives you a different perspective beyond the periodic table list and would love to see this expanded into a colour chart of elements and there relationships.
Which is interesting as many are describes as Silver in colour, though very few yellow (sulphur, chlorine) and Gold being described as gold. Though that is the only metal yellow and with that would possibly explain its unique colour.
On a side note I recall in the early days the fuss about creating that perfect gold colour with R,G,B and the arguments abound with whos gold was gold and whos was yellow. With that it is a fascinating colour and one that not easily replicated.
It was an early source of amazement for me to learn that we could actually calculate the colours of certain substances from their electron transitions (albeit with some empirically determined constants). A diagram, an equation, a few constants, and boom, you have the actual colour of a substance that matches your real-life observations. For reasons like this, I was quite into chemistry for a few years in high school.
It's a demonstration of our ability to discover the principles of reality and make meaningful predictions, rather than merely observe and catalog nature as our ancestors did. It's one of the wondrous aspects of science for me.
I've read the (900 page) Autodesk Files a couple times, but didn't realize how many other topics John Walker has written about. If you look through this site, there's even some fiction.
It may be forgivable to use dynamic mass in an article written for laymen and using a simple model of the atom, but I feel I should mention that the concept of objects changing mass depending on the reference frame is a very dangerous one because substituting the dynamic mass for the mass in a classical formula does not always lead to correct results.
The concept of dynamic mass is motivated by wanting to continue to write the previously known three-momentum as p = m v, which does not conform to special relativity, hence the definition of mass is changed. However, in a formula as basic as F = m a (F and a being vectors), substituting the dynamic mass for m does not yield correct results because in general, under special relativity, F and a do not even have to be parallel.
Modern formulations of dynamics in special relativity use the more intuitive invariant mass, and three-momentum is written as p = m gamma v, where gamma is the factor previously included in m_r. This p is now the spacial components of four-momentum p^\mu = m u^\mu, where m is the invariant mass and u is the relativistic four-velocity of the moving object.
The article is correct. The nit from grandparent is, that it uses some outdated language. So if you do not look to closely in special relativity, you will find that the mass quite often appears together with the Lorentz factor, which describes time dilation. This lead historically to the claim that moving objects are heavier than the same object at rest. But since this does not hold in general relativity, it is nowadays usually assumed that mass is always the rest mass. And so the article reads a bit outdated.
Start off with this: relativity is complicated, and unintuitive from the standpoint of human experiences.
So, let's talk about gravity. Gravity is a force between objects which have a certain kind of property, let's call it property X. Gravity has a precise quantitative relationship with property X, the more property X an object has the more gravitational force it exerts.
What is "property X"? It's energy. And here is where things get a bit complex, because most people would instead have said that "mass" is property X. The problem with that is mass becomes variable depending on the reference frame, and it turns out to add a lot of excessive complexity to discussing things, especially when precision is required.
So you could imagine talking about mass as the equivalent of energy, which is typically an accurate viewpoint, and then you get to the idea of "relativistic mass". Which is the adjusted "property X" value of an object which might be traveling at relativistic speeds in a given reference frame.
Relativistic mass, or property X, can be a helpful mental model in some ways, and in normal uses of English it's often a more useful way of thinking about things. But it's also problematic because it's ambiguous.
This has led to a bit of an impedance mismatch between the way physicists talk about relativistic effects and the ways that it's more natural to talk about such things in plain English. In English "property X" is mass, but in physics it's actually energy, and it's difficult to get people to fully grok the intimate relationship between energy and mass.
Physically, mass is just a special name for invariant, or rest, energy, the energy of an object in the reference frame where the object is stationary. It's all energy, but it's important to separate out rest-energy vs. energy in a given reference frame, and so forth.
p^μ is the μ-th component of the vector p, and in an equation p^μ = m u^μ, μ is to be taken as a free variable, i.e. the equation is true for every μ. In relativity, Greek indices are taken to range over time and the three spacial dimensions (whereas Latin indices only range over the spacial dimensions).
This notation can be naturally extended to tensor products of vectors in the tangential and co-tangential spaces to the base manifold that is spacetime (simply called "tensors" by physicists): https://en.wikipedia.org/wiki/Einstein_notation
I like how the article starts by saying GPS hides too many details from the user to be a good relativity example, and then dives into the "easier" example of gold being yellow by explaining the electron distribution probability function. That's much easier to grasp, thanks!
NOVA had a show on medieval stained glass that showed the size of gold particles trapped in glass created different colors. If the mass and electron distribution of gold is solely responsible for its color then shouldn't the size of gold particles (above 1 atom in size) have no effect?
You're right, the colour of materials is much more complex than just the available atomic transitions. The electronic states are changed and spread out by being bonded to other atoms and you get bulk collective properties like polarizability. The relativistic contraction mentioned in the article is still relevant for the electrons' energy levels in bulk gold (a big lump much larger than the wavelength of visible light) and so neglecting it would give the wrong colour for bulk gold.
Structures up to a few hundred nanometers in size could also conceivably affect the colour. This is kind of like how the atomic-level description of a radio antenna doesn't really matter, more its bulk properties like conductivity. The gold nanoparticle effect is due to Mie scattering (http://en.wikipedia.org/wiki/Mie_Scattering), which is the scattering of light off dielectric spheres approximately the size of the wavelength of light. This effect isn't relevant if you just have a brick of gold.
(solutions of CdSe nanoparticles in order of increasing particle size)
Broadly speaking, since "colour" isn't a well defined for things like atoms, but it is for macroscopic objects, it makes sense that there's some weirdness that goes on for particles in between those two extremes.
The color change of gold and CdSe particles with size are due to two different effects.
CdSe is a semiconductor, and reducing the CdSe nanoparticle size increases its band gap through a process called quantum confinement. For smaller particles, it requires a photon to have higher energy (i.e. smaller wavelength) to be absorbed.
Gold particles derive their color from the scattering mechanism mentioned in the parent comment.
Completely agreed; I was just providing another example for how the colour of large objects does not necessarily have anything to do with the colour of small objects. Thanks for the added context :)
23 comments
[ 2.9 ms ] story [ 58.8 ms ] threadCertainly for non oxided elements, Bismuth being a wonderful element colour wise with oxidisation in effect.
I do enjoy articles like this as they explain the more common building blocks of elements in a way that gives you a different perspective beyond the periodic table list and would love to see this expanded into a colour chart of elements and there relationships.
Had quick look and found this: http://periodictable.com/Properties/A/Color.html
Which is interesting as many are describes as Silver in colour, though very few yellow (sulphur, chlorine) and Gold being described as gold. Though that is the only metal yellow and with that would possibly explain its unique colour.
On a side note I recall in the early days the fuss about creating that perfect gold colour with R,G,B and the arguments abound with whos gold was gold and whos was yellow. With that it is a fascinating colour and one that not easily replicated.
It's a demonstration of our ability to discover the principles of reality and make meaningful predictions, rather than merely observe and catalog nature as our ancestors did. It's one of the wondrous aspects of science for me.
http://www.fourmilab.ch/autofile/
The concept of dynamic mass is motivated by wanting to continue to write the previously known three-momentum as p = m v, which does not conform to special relativity, hence the definition of mass is changed. However, in a formula as basic as F = m a (F and a being vectors), substituting the dynamic mass for m does not yield correct results because in general, under special relativity, F and a do not even have to be parallel.
Modern formulations of dynamics in special relativity use the more intuitive invariant mass, and three-momentum is written as p = m gamma v, where gamma is the factor previously included in m_r. This p is now the spacial components of four-momentum p^\mu = m u^\mu, where m is the invariant mass and u is the relativistic four-velocity of the moving object.
So, let's talk about gravity. Gravity is a force between objects which have a certain kind of property, let's call it property X. Gravity has a precise quantitative relationship with property X, the more property X an object has the more gravitational force it exerts.
What is "property X"? It's energy. And here is where things get a bit complex, because most people would instead have said that "mass" is property X. The problem with that is mass becomes variable depending on the reference frame, and it turns out to add a lot of excessive complexity to discussing things, especially when precision is required.
So you could imagine talking about mass as the equivalent of energy, which is typically an accurate viewpoint, and then you get to the idea of "relativistic mass". Which is the adjusted "property X" value of an object which might be traveling at relativistic speeds in a given reference frame.
Relativistic mass, or property X, can be a helpful mental model in some ways, and in normal uses of English it's often a more useful way of thinking about things. But it's also problematic because it's ambiguous.
This has led to a bit of an impedance mismatch between the way physicists talk about relativistic effects and the ways that it's more natural to talk about such things in plain English. In English "property X" is mass, but in physics it's actually energy, and it's difficult to get people to fully grok the intimate relationship between energy and mass.
Physically, mass is just a special name for invariant, or rest, energy, the energy of an object in the reference frame where the object is stationary. It's all energy, but it's important to separate out rest-energy vs. energy in a given reference frame, and so forth.
What's the backslash, is that m times u or μ, is that exponentiation, which are vectors and which are scalars?
mu is being used as an index (mu=0,1,2,3) on the components of the vectors p and u, m is a scalar representing rest mass.
This notation can be naturally extended to tensor products of vectors in the tangential and co-tangential spaces to the base manifold that is spacetime (simply called "tensors" by physicists): https://en.wikipedia.org/wiki/Einstein_notation
http://www.pbs.org/wgbh/nova/ancient/science-stained-glass.h...
Structures up to a few hundred nanometers in size could also conceivably affect the colour. This is kind of like how the atomic-level description of a radio antenna doesn't really matter, more its bulk properties like conductivity. The gold nanoparticle effect is due to Mie scattering (http://en.wikipedia.org/wiki/Mie_Scattering), which is the scattering of light off dielectric spheres approximately the size of the wavelength of light. This effect isn't relevant if you just have a brick of gold.
http://education.mrsec.wisc.edu/background/quantum_dots/imag...
(solutions of CdSe nanoparticles in order of increasing particle size)
Broadly speaking, since "colour" isn't a well defined for things like atoms, but it is for macroscopic objects, it makes sense that there's some weirdness that goes on for particles in between those two extremes.
CdSe is a semiconductor, and reducing the CdSe nanoparticle size increases its band gap through a process called quantum confinement. For smaller particles, it requires a photon to have higher energy (i.e. smaller wavelength) to be absorbed.
Gold particles derive their color from the scattering mechanism mentioned in the parent comment.
The second comment has a link to to the spectrum comparison between gold and silver.
http://commons.wikimedia.org/wiki/File:Image-Metal-reflectan...
(Found via a comment in the earlier submission[0] and discussion of this item. Thanks to gus_massa[1] for finding that[2].)
[0] https://news.ycombinator.com/item?id=1246065
[1] https://news.ycombinator.com/user?id=gus_massa
[2] https://news.ycombinator.com/item?id=6874210
You may also recall this article about the nature of mercury: http://blogs.scientificamerican.com/the-curious-wavefunction...