Why are gold nanoparticles red? While watching the latest computerphile video (https://www.youtube.com/watch?v=FGiBHsUkVzU)  I came across a solution of nanoparticles of gold
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but to my surprise, they appeared as red, shouldn't gold be golden color? 
 A: The answer is that spherical gold nanoparticles are indeed very red, if there size is sufficiently small -- smaller than the actual wavelength of red light (<~600nm). A typical size would be 100nm.
The effect is due to the scattering cross section of photons with different wavelength from those particles. Since these are metallic spheres, there are mini electron-clouds inside. For such nano scale spheres there are resonances of the electron clouds excited by incoming photons. For gold the resonance peak wavelength is a few times larger than the actual size of the spheres but has a pretty wide range where it drops for shorter wavelengths. This means it appear very red, because it is a very efficient scatterer for red wavelength.
The color actually depends on the size, as well as the shape.
A: One thing to note : red back background.  How much is that affecting the appearance ?  Certainly their will be a great amount of red light to be reflected by the water, glass and particles in the water.  Hard to know if this effect is significant or not in this case.
Part of the color (the spectral response) you see in metallic gold is due to the energy levels structure of the metal structure.  The spectrum of atomized gold is a different thing.  In a liquid suspension, you are seeing another set of complex interactions and the metallic structure is not likely as significant.
So this appearance is a combination of multiple factors.
This webpage does describe some of the properties of gold nanoparticles, including the varied color appearance and why that is.  One statement is :

A major determinant of the optical properties of gold nanoparticles is their shape. By synthesizing gold nanoparticles of different shapes, the surface plasmon resonance can easily be tuned to give absorption maxima from around 500nm into the near-infrared part of the spectrum.

A: The phenomenon is called Localized Surface Plasmon Resonance (LSPR).
In a nutshell: a plasmon is a charge (quasi) particle oscillation. In the case of light reflecting at an interface between a dielectric (e.g., like your liquid) & a metal,the SPR is excited in the metal and confined to the surface.
Gold nanoparticles suspended colloidally (like yours) are so small, that part of the surface fulfill the conditions for SPR regardless of the light direction. The size of the particle strongly influences the color.
The stained glass window in the Notre-Dame cathedral in Paris uses this effect for some colors.
If you‘re really interested check out this review paper: doi: 10.1088/1361-648X/aa60f3.
