### Why is ionic solution transparent when conducting electricity?

4 days, 10 hours ago

```At first glance, this question is meaningless, but it is interesting to think about it carefully.

From life experience, we know that brine is conductive and transparent. But if you think a little deeper, you can see that the word "transparency" is related to wavelength. As mentioned in other answers to this question, water and salt water absorb infrared light. Another example is that glass absorbs ultraviolet light. Conversely, X-rays and gamma rays can also pass through metals. Moreover, "transparency" must be related to "thickness". Even in visible light, the extremely thin gold coating is transparent, which is often used as anti laser goggles. Even the clearest sea water is dark below 10 meters.

Therefore, this sentence given by the subject

the transparent material must be an insulator because of the Joule heat loss caused by the electromagnetic wave passing through the conductive material.

What does that mean?

The subject of the book is Max Born's "principles of optics", the author is well-known, not to be scribbled. So I went to the context of the book, such as section 1.1.4 mentioned in the paper, and the subsequent reference to "the propagation of light in conductors" (Chapter 13)

First of all, I noticed that born wrote this sentence on the premise of ignoring the boundary conditions

here the heat q is defined as

Born said that the insulator is the conductivity σ = 0, so when
propagates within the object
, it will not produce Joule heat. In contrast, it means that the conductor will produce Joule heat and eventually consume the energy of electromagnetic wave.

Therefore, the "opaque" conductor mentioned by born here means that the boundary conditions are ignored, that is, the conductor with
infinite thickness
So, in this context, the solution is really opaque. In my opinion, instead of distinguishing between "conductor" and "insulator", he strictly distinguishes σ = 0 and σ ≠ 0
. How to say this logic Hum

In practice, except for absolute vacuum, where is σ strictly equal to 0? Even air, if there is a certain amount of free ions, will become a "conductor" (ionosphere).

By chapter 13 of the book, born begins to deal with the case of
σ≠ 0
. Then you'll see the treatment of surface reflection - which was completely ignored in the discussion in section 1.1.4 above. In the interior of the conductor, we have
penetration depth

<img class="content-image" src=" https://pic3.zhimg.com/v2-a27fd37352110d7f8f2a19bea01a6bba_ b. It can be seen that the higher the conductivity of the conductor, the smaller the penetration depth; the lower the conductivity, the greater the penetration depth. However, for the same conductor, how does the conductivity of ionic liquids compare with that of metals?

conductivity of sodium chloride solution

metal conductivity

the conductivity of salt water



, which is 7 orders of magnitude lower than that of metals!
naturally, the penetration depth of ionic solution is at least three orders of magnitude higher than that of metals. The metal film with a thickness of 1 mm is opaque, but the ionic solution with a depth of 1 m can still be transparent.

However, the skin depth formula is an approximate formula, and its approximate condition is that the frequency of light is low enough
: σ≫ε ω. In the physical picture, the propagation of electromagnetic wave in the conductor will drive the free charge movement in the conductor, and the conductivity σ is related to the maximum velocity of the free charge movement in the conductor. Therefore, this approximate condition says that the frequency of the vibration of the free charge in the conductor is much higher than that driven by the external field; in this way, the free charge can perfectly resonate with the electromagnetic wave.

You may be surprised that the conductivity σ itself is also related to the frequency of light:

here, β is the maximum velocity of free charge in the conductor. When ω is small enough, σ is approximately a (large) real number; when ω is large enough, σ begins to have a considerable imaginary part. This means that the free charge in the conductor can not keep up with the vibration of the electric field and begin to produce hysteresis. And once there's a lag - it's like an insulator.

This transition frequency is the "plasma frequency" of the conductor. Beyond this frequency, the conductor will become "transparent" and "plasma oscillation" will occur. This frequency is equal to

Where n is the density of the free charge, q is the amount of charge, M is the mass of the free charge, and ε is the dielectric constant.

In metals, the free charge is the free electron, so m is the electron mass. In ionic solution, the free charge is the charged ion, so m is the mass of the ion. Notice that the mass of a proton is 1800 + times the mass of an electron. How much should an ion in the solution weigh? Therefore, < img class = "content image" SRC=“ https://www.zhihu.com/equation?tex=%5Comega_ It is 2-3 orders of magnitude lower than metal.

In general, the
in the ultraviolet region (λ ~ 100-300 nm, ω ~ 10 ^ 15 Hz). Therefore,
is reduced to the infrared region (λ ~ 100-300 μ m, ω ~ 10 ^ 12 Hz). The sum of this value and
@ drapeaublanc
are qualitatively consistent.

What's fascinating about all the above discussions is that they are completely based on the same set of equations directly derived from Maxwell's equations. The difference is that the conductivity σ of a substance is different, which will show a completely different phenomenon. From the microscopic point of view, that is, whether the velocity of the free charge in the material (or expressed in terms of the average free path) can keep up with the vibration of the electromagnetic wave, which determines whether the matter is transparent. Therefore, whether it is free electron, metal, plasma gas, ionic solution The same set of physical laws can explain their behavior well, despite the ever-changing physical systems.

Of course, all of the above discussions are carried out in the abstract physical picture of "free charge", and there is no specific absorption of light by vibration and rotation of specific molecules. This involves a lot of contents of spectroscopy, so it will not be expanded.

Finally, combined with my own thoughts on translating Schr? Dinger's books, I think the words and logic of German books are really hmm…… I'm crazy about Regarding the transmission of light in matter, I think the Feynman handout

is more interesting and easier to understand. To quote Feynman:

Although we have been talking about wave propagation in metals, you appreciate by this time the universality of the phenomena of physics—that it doesn't make any difference whether the free electrons are in a metal or whether they are in the plasma of the ionosphere of the earth, or in the atmosphere of a star.```

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