# Confusion about the light and the transparency of objects

I am so confused about the interaction between the photon and the atoms especially when we see it and perceive the color. I think there are many questions like this before but I still don't understand its answer since I can't picture what happened in the atom when we see things.

As it is mentioned that the atom is almost empty so the photon should pass through it easily but things are opaque and I want to understand why.

There are some explain that when photon has exact energy to excite an electron in the atom to jump into the higher state then electron absorbed it and no light in that frequency passes through the atom.

1. The exact value means greater than or equal so that the electron can be excited into the higher level? If not why the greater energy cannot excite the electron and just let the excess energy go somewhere?

2. The above statement still is unclear to me because the atom filled with space so why photon can interact with the electron? The probability for them to meet should not be high? Or is it because of the cloud atomic model that they somehow can have a high probability to interact with each other?

3. If it is the case that electron is excited into the higher state, assume that the object appears blue, then all except blue wavelength photon will be absorbed each by corresponding electrons? Does it mean that many electrons get excited and jump into the higher state (corresponding to their exact energy photon that they absorbed)?

4. Why doesn't electron jump back to its original state? Because if it jumps back to its original state it should emit energy the same amount it absorbed, which then can be combined with all other electrons to be appeared almost white(except blue)?

5. If 3. is the case then the atom that electrons jump to the lower positions (but higher than its original) will have to be excited (next time) by the photon with higher energy than before (since it's in the higher state than original) and hence we should see the object with the different color than before?

I think maybe this fails at the very first question so someone please explain the interaction step by step for this (color perception) phenomena?

Some substances do absorb photons of just the right frequency. When you shine a white light on them, you see sharp absorption lines in the spectrum of the reflected or transmitted light.

The excited atoms may decay and emit the light again. If they do, they emit in all directions.

Sometimes they decay in more complex ways. For example, a fluorescent atom may absorb UV light and emit visible light. Some molecules may excite vibrational states instead of emit light.

But not all color is explained by single atom processes. See If we repeatedly divide a colorful solid in half, at what point will the color disappear?

Sometimes it is less confusing to think about photons and sometimes about waves.

• Thank you, I google for the spectrum line of the hydrogen atom. In the Rydberg equation, the line in the emission spectrum satisfies the equation with the ground state of 2. Why does the ground state of the electron in the hydrogen atom be 2 instead of 1? Commented Jun 5, 2021 at 4:04

First off, you must be careful to avoid too sticking too much to a classical picture where the atom is mostly "empty" and the photon is a point particle that you imagine should "pass through it easily".

1. Texts that state that the photon needs exactly the right energy to excite the electron may be trying to keep things simple, but I believe are just sowing confusion. The truth is that the photon only needs close to the right amount of energy to excite the electron. The more technical answer is that the photon has a certain probability of exciting the photon from state A to state B, and this interaction cross section has a (roughly) Breit-Wigner resonance at the energy difference between the two states.

2. Neither the photon nor the electron are point particles and they are able to interact quantum mechanically when their wavefunctions overlap appreciably in space. (Or, depending on your point of view, we know empirically that they do interact and describe this quantitatively using wavefunctions that overlap in space).

3. I don't quite follow this question.

4. Yes, the electron can jump back down directly to its original state and re-emit a photon; it can also jump back down in several steps, emitting photons of lower frequency.

• Thank you 0. Does this mean that we can give the excess energy to excite it and need not be exact(or nearly exact)? 1. This means that the probability that their wavefunctions overlap appreciably is close to 1 if we consider the whole substance for the opaque object? Commented Jun 5, 2021 at 3:08

This is a deep question that can be treated at different levels of sophistication. I won't attempt to provide a complete answer, but I can chime in with some information that I hope is insightful.

The most basic level of understanding comes from the classical picture of light as a wave in the electromagnetic field. (1) electrons (and all charged particles) emit electric field lines. (2) electrons (charge $$q=-e$$) feel a force $$\vec{F}$$ in the presence of an electric field $$\vec{E}$$: $$\vec{F} = q\vec{E}$$ The electrons in matter are pushed around by electric fields, and waves in the electromagnetic field (light) will cause them to jiggle.
(3) The jiggling electron then emits its own wave in the electric field. This is the "reflected light" from the material.

This simple picture provides some insight into why, for example, good conductors that have lots of free electrons tend to be shiny: they readily respond to the force exerted by the oscillating electric field as the wave "washes over them" and therefore start jiggling at the same frequency, reflecting the light that is incident on the conductor. In the quantum picture, the electron states in a conductor form a continuous "band" of energies so they can absorb photons with a continuum of energies.

A useful classical picture for an atom in an insulator is an electron attached to a heavy nucleus by a spring; it's no longer free like it is in a conductor. The oscillator has a resonance frequency and will respond strongly if the electromagnetic wave jiggles it at its resonance frequency. A material made of such an atom would be transparent at frequencies different from the resonance frequency, but would reflect strongly at resonance.

I hope that this provides a simple classical picture that strengthens your intuition here. The issue of color is very complicated. See fore example,

https://www.amazon.com/Physics-Chemistry-Color-Fifteen-Applied-ebook/dp/B000YIUP5S

• Thank you, I like the way you describe about the conductor. Does it mean that the color we perceive, in the classical view, is the resonance frequency that the electrons in the matter jiggle? If so then the shiny we perceive is its amplitude? In classical picture involving a conductor, Does this mean that free electron, which is readily respond the field from the light, will jiggle in a more amplitude way so the conductor tends to be shinier? Commented Jun 5, 2021 at 4:02
• The color that we will perceive corresponds to whatever light is reflected back to us by the material. For a conductor, that's pretty much all of the light, so it looks like a mirror surface. For an insulator, the question is much more complicated, but loosely speaking the material only reflects light at particular "resonant" frequencies. There can be a lot of resonances, however, in a material, and the color we perceive is a combination of all the reflected frequencies. Commented Jun 7, 2021 at 22:06