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Special Relativity and Gold

2025-02-14 Update From: SLTechnology News&Howtos shulou NAV: SLTechnology News&Howtos > IT Information >

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Objects have color because their electrons resonate most strongly with certain wavelengths of light, which they absorb and reflect back to our eyes at all other wavelengths. Most metal electrons resonate most strongly with ultraviolet light, so they reflect all wavelengths of visible light equally, which makes them silver. But gold is different, it presents a noble gold, in order to explain the difference between gold and other metals, we need to apply the special theory of relativity.

According to Einstein's special theory of relativity, the faster an object is, the greater its mass will become. In light atoms such as hydrogen, which have only one proton and one electron, the electrostatic force is very weak, so the electrons move very slowly around the nucleus. But gold has 79 protons in its nucleus, so electrons are attracted by huge static electricity. To avoid colliding with the nucleus, the innermost electrons need to travel at half the speed of light. When the speed of an object becomes so fast, the relativistic effect becomes crucial: the electron mass increases by about 20%, which has a direct effect on the atomic radius of the electron orbit: the orbital radius decreases.

So far, we have been using the Bohr model of atoms, which assumes that electrons move around the nucleus, just as planets move around the sun. But to get to the bottom of it, we need to use a more accurate but more complex quantum model. In this model, orbital electrons are replaced by probability clouds, which show where electrons are most likely to appear.

The electron closest to the nucleus is on the 1s orbital, and the next orbital is the 2s orbital. All in all, it has six s orbitals, all of which are spherical. But not all electronic orbitals are spheres. Other orbitals, such as p orbitals, look like two balloons, while d and f orbitals look even weirder.

If you look closely at the s orbitals, you will find that the probability distribution is not evenly distributed. Electrons are likely to be closer to the nucleus because they like to be in a lower energy state. The areas where electrons are most likely to be found are called probability peaks, and the probability peaks of all s orbitals are very close to the nucleus. As we discussed earlier, being close to the nucleus means that electrons move at hypervelocity, which means that all six s orbitals of gold atoms contract relativistically.

But the probability peak of the d orbital is farther away from the nucleus. Because they do not feel strong attraction, they do not reach very high speeds, so they are not affected by this relativistic contraction. More importantly, as the electrons in the s-orbital bind more closely to the nucleus, they also act as an electrostatic shield. So the electrons in the farther d orbitals feel the weaker force from the nucleus and further expand the radius.

In this quantum model, the absorption of wavelengths also occurs between orbitals. Most metals have peak absorption wavelengths in the ultraviolet spectrum, which means that they reflect all visible light. For gold, this absorption occurs between 5d and 6s orbitals. The electrons in the 5d orbit will absorb photons of a certain wavelength and jump to the 6s orbit. If relativity is not taken into account, the energy required to jump from a 5d orbit to a 6s orbit will correspond to the frequency in the ultraviolet spectrum, just like other metals. But because of the relativistic effect, the 6s and 5d orbitals are closer together, and scientists have measured their frequencies corresponding to blue and purple light.

By absorbing blue and purple light and reflecting the rest of the visible light, gold shows a noble yellow. Why other more heavy metals (such as mercury and lead) do not occur is because their peak absorption wavelengths are not in the Goldilocks zone.

This article comes from the official account of Wechat: Vientiane experience (ID:UR4351), author: Eugene Wang

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