H atom's excited state lasts on average $10^{-8}$ secs, is there a time gap (of max 2*$10^{-8}$ secs) betwn. two consec. photon absorpt.-emiss. pairs?

OK here is a description of what happens:

1. time=0,timer starts
2. first absorption happens,
3. first emission happens
4. absorption #2 happens
5. emission #2 happens, stop timer
6. timer==?

According what I found, step 2+3 lasts max average $10^{-8}$ secs.

Step 2+3, should equal to a H atom's first excited state's avarage lifetime should be around $10^{-8}$ secs. $^{[a]}$

According to QM, theoretically the emission of a photon by the electron of the H atom is instantaneous.

So since the excited state itself lasts $10^{-8}$ secs in between the (theoretically instantaneous ) emissions , there should be a time gap between the emission of two individual photons.

According to accepted theory a photon is a quanta of light, interpret-able/measurable as an individual.

Question:

1. what will be the timer's value after stopping at step 6?
2. Am I correct that the timer will be equal to max 2*$10^{-8}$s gap between the emission of individual photons? (NOTES: The lifetime of $10^{-8}$ is for an absorption-emission pair. I am asking about the gap between two consecutive absorption-emission pairs (so basically between two consecutive emissions). So the 2nd emission (which is instantaneous itself )can only happen max 2* $10^{-8}$ secs after the first emission?)

Just to be VERY clear, the value of the timer that I am asking for is equal to this question: how soon after the excited state decays to the ground state can the ground state absorb another photon and go back to the excited state?

1. Is this also causing that, since between two emissions, the electron is moving, the direction of the emissions of the individual photons will be randomly different in case of two photons emitted after each other?
2. Is there any way to measure this gap, somehow by the absorption of the photons on a round surface (all around the light source) and by recording the timing of the absorptions?
• Even after your edit the question still doesn't make sense. I think you need to give us a detailed timeline of the processes you are thinking about i.e. a step by step description of what is happening. – John Rennie Oct 14 '16 at 17:23
• OK I think you're asking how soon after the excited state decays to the ground state can the ground state absorb another photon and go back to the excited state. Is that correct? – John Rennie Oct 14 '16 at 17:40
• what you say +go back to ground again(so emit again). Just because what you say I think would be instantaneous. so the full circle, with absorption, emission,absorption, emission. Like: the timer starts right before the first absorption, and stops after the second emittion. – Árpád Szendrei Oct 14 '16 at 17:49
• the only difference between what you say and me is that your timer starts after the first absorption, and stops before the 2nd emission. Mine starts before the first absorption and stops after the 2nd emission. But you might be right, because the absorption and the emission themselves are instantaneous. – Árpád Szendrei Oct 14 '16 at 17:51
• so yes, your version and mine need the same time to happen. thank you for your help. Now we just need to figure out the answer. Is it max 2*10(-8) or just max 10(-8)? – Árpád Szendrei Oct 14 '16 at 18:02

According to QM, theoretically the emission of a photon by the electron of the H atom is instantaneous.

This is wrong, there is nothing instantaneous in quantum mechanical theory. All knowledge comes from measurements, and all measurements correspond to quantum mechanical operators which give the expectation value of what one is measuring. Everything is probabilistic on an individual particle/atom level.

So let us see whether the measurement you envisage can be done consistently with quantum mechanical conditions.

time=0,timer starts

This cannot happen on an individual atom level. There is no way to define a time without disturbing the atom, and thus changing the boundary conditions. One can have a number of hydrogen atoms in a volume.

first absorption happens,

One can throw one appropriate energy photon at a hydrogen aggragate, and see that it has been absorbed, i.e. does not register behind the hydrogen sample. All one knows is that some single hydrogen is now at an excited state.

first emission happens

If one waits with the appropriate instruments , one will catch the emitted photon, but will not know which atom it came from ( except within the Heisneberg uncertainty principle, delta(p)*delta(x), this will be a large volume, and avogadro's number is of order ~10^23 .

absorption #2 happens

this cannot happen because you cannot find the hydrogen atom that underwent absorption #1

emission #2 happens, stop timer

this is not doable.

I do not know whether progress in nanotechnology can trap single identifiable hydrogen atoms, so that one might excite one, wait to catch the decay and send the second photon. Still your program will not work, because the first photon will leave with a probability within the time decay probability curve , not a fixed number for all atoms. Also the behavior with a quantum mechanically trapped hydrogen will be different than with a free hydrogen, and lots probabilities will affect the timing.

So this is a non doable thought experiment.

Now on how soon a de-excited atom can be re-excited can be estimated from the width of the excited state and the crossection of atom+photon interaction. Since it is electromagnetic it will be of the order of electromagnetic interactions , ~1o^-8 seconds

• Comments are not for extended discussion; this conversation has been moved to chat. – ACuriousMind Nov 30 '16 at 0:51