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### Author Topic: How much time does it take for an electron to emit a photon?  (Read 1757 times)

#### rolsen

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##### How much time does it take for an electron to emit a photon?
« on: 02/02/2016 20:48:04 »
I have never see the time it takes for an electron to emit a photon addressed in any of the physics courses I've taken.  There is a lot of information on how an electron emits a photon: by falling or transitioning from a higher energy level or orbit to a lower energy level or orbit, etc.  But does not this transition take time?  How long does it take for an electron to 'move' or 'fall' from a higher orbit to a lower orbit?  Along its journey it might instantaneously emit a photon, but it still seems like it would take some time to make the trip.

#### chiralSPO

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##### Re: How much time does it take for an electron to emit a photon?
« Reply #1 on: 02/02/2016 21:24:49 »
Electrons don't have to physically move to change energy levels. In fact, my understanding is that they must not move during these transitions--and it is easier for an electron to move between orbitals that have more spacial overlap than between orbitals that have little spacial overlap.

For the sake of simplicity, imagine an isolated hydrogen atom in the ground state. There is one proton in the nucleus, and one electron in the 1s orbital. The 2s and 3s orbitals are, overall, more diffuse than the 1s orbital, but both have significant electron density close in to the nucleus, where the 1s is. Take a look at the attached radial electron density map (attached image entitle orbitals.jpg)

Therefore, since the electron does not have to actually move, it is entirely possible for the change to take place instantaneously. Take a minute to think about why it makes sense that it would have to happen instantaneously (from a QM perspective).

#### chiralSPO

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##### Re: How much time does it take for an electron to emit a photon?
« Reply #2 on: 02/02/2016 21:56:43 »

Even if the actual emission is instantaneous, it is still worthwhile to talk about the rate at which a population of excited atoms or molecules (or a bulk material) relax and emit photons.

Usually people talk about the lifetime or half-life of an excited state. For instance, fluorescent molecules usually have a long (relatively) lifetime, on the order of microseconds. Other molecules may relax within a picosecond or less...

#### evan_au

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##### Re: How much time does it take for an electron to emit a photon?
« Reply #3 on: 03/02/2016 09:10:10 »
Quote from: rolsen
I have never see the time it takes for an electron to emit a photon addressed
One important electron transition for radio astronomy is the 21cm Hydrogen line, where the electron in a hydrogen atom flips from being parallel to the nucleus to facing the other way.

It is estimated that this transition occurs about once in 10 million years.

The fact that this event is so rare allowed radio astronomers to map the gas clouds in the arms of the Milky Way galaxy, and map the density of matter between Earth and distant quasars.

See: http://en.wikipedia.org/wiki/Hydrogen_line#Cause

#### evan_au

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##### Re: How much time does it take for an electron to emit a photon?
« Reply #4 on: 05/02/2016 11:03:39 »
Some work at the Max Plank Institute (and others) suggests that electrons may respond to photons on a timescale of around 100 attoseconds.

http://spectrum.ieee.org/tech-talk/semiconductors/optoelectronics/fastest-light-pulses-show-that-electrons-react-slowly-to-light

#### chris

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##### Re: How much time does it take for an electron to emit a photon?
« Reply #5 on: 05/02/2016 11:29:55 »
When an electron becomes "excited", where is the energy "stored", and as what?

#### chiralSPO

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##### Re: How much time does it take for an electron to emit a photon?
« Reply #6 on: 05/02/2016 17:18:00 »
When an electron becomes "excited", where is the energy "stored", and as what?

There are multiple contributions to the energy of an electron in an orbital. Let us consider atomic orbitals for now, and then think about extending to molecular orbitals.

Atomic orbitals are defined by the quantum numbers, the first 2 of which are the major factors in energy:

The principle quantum number (n) can be thought of as a pure electrostatic term, signifying the average distance between the electron and the nucleus. The farther apart they are the more electrostatic potential energy is stored (just like gravitational potential energy).

The secondary quantum number (l) signifies the angular momentum of the electron, you can think of this as internal kinetic energy (classically, how fast the electron is moving around the nucleus).

The other two quantum numbers do contribute to the energy, but in more complex ways (especially relevant in systems with multiple interacting electrons).

Molecular orbitals are much more complex, and harder to wrap one's head around. But we can borrow tricks from matrix algebra, and show that molecular orbitals are linear combinations of atomic orbitals of each of the constituent atoms, and because of various conservations laws, we can also add up the energies and angular momenta of each of the constituent orbitals, and know that the rules and trends are the same.

#### agyejy

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##### Re: How much time does it take for an electron to emit a photon?
« Reply #7 on: 06/02/2016 00:14:13 »
I can't give an active link but here are some urls (a direct copy paste should work):

www3.uji.es/~planelle/APUNTS/ESPECTROS/jce/JCEphoto.html - This is a very thorough explanation of absorption of photons with quicktime videos.

webpages.ursinus.edu/lriley/courses/p212/lectures/node40.html - This is another explination of the absorption process.

The gist of the above is that in order for an electron to transition from one state to another it has to enter a supposition of the initial and final state. The resulting supposition is no longer time independent and evolves over a finite amount of time from being more initial state to being more final state with significant oscillations. The result for an electron in an atom is that the electron cloud changes shape in an oscillatory manner with a frequency that matches the light being emitted or absorbed.

The reason most physics courses don't talk about this processes is because it requires some pretty complicated mathematics (even by Quantum standards) and in general you can calculate everything you are likely to need to know about the absorption of a photon without ever detailing the processes. Most physical observables of interest like the energy of the photon can be calculated from the time independent stationary states so there is no reason to bother with the more complicated stuff.

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##### Re: How much time does it take for an electron to emit a photon?
« Reply #7 on: 06/02/2016 00:14:13 »