EXTRA CREDIT QUESTION (1 pt): Most metals have a “metallic” color, and when poli

Question

EXTRA CREDIT QUESTION (1 pt): Most metals have a “metallic” color, and when polished, become very shiny. However, some metals like copper and gold have a different color. Explain why you think the colors of these two metals are so different from the rest?

Note: if you go to the book, page 844, you will see that it says “Copper and gold appear red-orange and yellow, respectively, because some of the energy associated with the light photons having short wavelengths is not reemitted as visible light”. This is not completely true, and does not cover all of the reasons why gold and copper has a color. To get credit on this question, you will need to tell me (a) why energy associated with photon having short wavelength is not remitted (or not remitted efficiently), and (b) if there are any other major reasons for the colors.

Explanation / Answer

It is hardly surprising that the answer to this question relies heavily on quantum theory, but most people will be surprised to hear that the full answer brings relativistic considerations into the picture. So we are talking quantum relativistic effects.

The quantum bit of the story tells us that the colour of metals such as silver and gold is a direct consequence of the absorption of photons by d electrons. This photon absorption results in d electrons jumping to s orbitals. Typically, and certainly for silver, the 4d5s transition has a large energy separation requiring ultraviolet photons to enable the transition. Therefore, photons with frequencies in the visible band have insufficient energy to be absorbed. With all visible frequencies reflected, silver has no colour of its own: it's reflective, an appearance we refer to as 'silvery'.

Now the relativistic bit. It is important to realize that electrons in the s orbitals have a much higher likelihood of being in the neighborhood of the nucleus. Classically speaking, being close to the nucleus means higher velocities (cf speed of inner planets in solar system with that of the outer planets).

For gold (with atomic number 79 and hence a highly charged nucleus) this classical picture translates into relativistic speeds for electrons in s orbitals. As a result, a relativistic contraction applies to the s orbitals of gold, which causes their energy levels to shift closer to those of the d orbitals (which are localized away from the nucleus and classically speaking have lower speeds and therefore less affected by relativity). This shifts the light absorption (for gold primarily due to the 5d6s transition) from the ultraviolet down to the lower frequency blue range. So gold tends to absorb blue light while it reflects the rest of the visible spectrum. This causes the yellowish hue we call 'golden'.

Gold is so malleable that it can be beaten into gold leaf less than 100 nm thick, revealing a bluish-green color when light is transmitted through it. Gold reflects yellow and red, but not blue or blue-green. The direct transmission of light through a metal in the absence of reflection is observed only in rare instances.

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