# B Electron scattering off of a nucleus

1. Dec 4, 2018

### metastable

If I'm scattering electrons off of an atomic nucleus, can I infer any information about the duration of time the electron was accelerating by looking at the wavelength of the emitted bremsstrahlung radiation? I am wondering if it would be possible to derive a time interval between electron acceleration start (T1) and acceleration end (T2) by looking at the bremsstrahlung photon frequency.

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2. Dec 4, 2018

Staff Emeritus
No. Sinjce the EM force is infinite in range, the electron is always accelerating.

3. Dec 4, 2018

### metastable

Can I derive the duration of time it took for the electron to substantially change its momentum vector as a result of the scattering (rather than duration of acceleration since the EM range is infinite)?

4. Dec 4, 2018

### snorkack

Even classically, there is no time interval. The curvature is continuous.

Then again, the curvature is concentrated in a definable timescale around the closest approach.

Suppose that the electron is initially "at rest" - at apoapse of a bound orbit passing close to the nucleus. Such as 100s orbital - principal quantum number 100, orbital quantum number 0.
What are legal results of bremsstrahlung?
Orbital quantum number must change by 1 by a selection rule. Therefore, 100s electron can go to some p orbital. Not 1p (no such orbital) and not 100p (no transition - same energy as 100s) - but 2p, 3p...99p are all options and all of them will happen, in some ratio.
If there is a transition to 1s, it immediately tells you that the initial orbital was some p orbital (all others are forbidden to transition to s). If there is a transition to 3, but no transition to any orbital 2, you can immediately tell that 2p was forbidden by a selection rule, 3d allowed - therefore the initial orbital was a f one.
Does the selection rule of orbital angular momentum only changing by 1 also apply to unbound orbits? And in case of unbound-unbound transitions, does it constrain energies of radiation emitted?

5. Dec 4, 2018

### metastable

Can I define a period of time during which the electron's rate of momentum vector change is greater than a defined value, such a 1/1000th rad/sec, then correlate the measured time between T1 and T2 with the photon wavelength?

6. Dec 4, 2018

### Staff: Mentor

If you treat the electron as classical particle you can, but then you won't get a good description of what is going on.

7. Dec 4, 2018

### metastable

Can I examine an electron-proton scattering event from detectors substantially in the center of mass rest frame, then calculate the inverse of the frequency of the emitted bremsstrahlung photon (1/hz -- seconds/cycle instead of cycles/second), then prove this isn't substantially the same time interval as the electron's flight time between points T1 and T2 (these points being defined by some momentum vector change rate threshold which is greater than XX.XXXrad/sec)?

8. Dec 4, 2018

### Staff: Mentor

Didn't we discuss this already? Do you expect the answers to be different just because you ask the same question in a different thread?

No you cannot.

9. Dec 5, 2018

### metastable

I’m confused because you said treating the electron classically I can define a period of time (T1 -> T2) in the electron’s trajectory during which the rate of mometum vector change is greater than xx.xxx rad/sec.

But then you’ve said I cannot find a consistent vector change limit of xx.xxx rad/sec where duration T1 -> T2 = 1/hz of the emitted bremsstrahlung photon.

So If the bremsstrahlung photon is emitted “instantaneously” (ie no emission duration) but the duration of electron vector change which is > xx.xxx rad/sec = T2 - T1, are you saying that there are durations of time during T1->T2 where the electron’s momentum vector is continuously changing while no radiation is produced?

Or if you’re saying both the electron momentum vector change and the photon emission are instantaneous, how can I change the vector of an object with mass instantly without requiring infinite power? My confusion only deepens...

Or looking at the bremsstrahlung equation E1 - E2 = hv are you suggesting the E1 - E2 side of the equation takes a duration of time (Duration T1 -> T2 >xx.xxx rad/sec momentum vector change rate) but the hv side of the equation is instantaneous?

Or if the energy/momentum vector of the electron continues changing after the photon is emitted, but E1 - E2 = hv — wouldn’t the electron’s change in energy/momentum occuring after the emission of the photon somehow need to be transmitted backwards in time to the region of the photon emission to satisfy E1 - E2 = hv ?

Last edited: Dec 5, 2018
10. Dec 5, 2018

### Staff: Mentor

If you treat things classically that you shouldn't you can calculate a lot of things that all have little to nothing to do with reality.

11. Dec 5, 2018

### metastable

Does it then follow that an electron also can absorb a photon with no absorption duration — instantly — in other words absorption occurs in less time than the photon takes to traverse its wave-length in a vacuum (wavelength meters/c)?

12. Dec 5, 2018

### Staff: Mentor

There is no well-defined duration for such a process and a free electron cannot absorb a photon (without also emitting one) anyway.

13. Dec 7, 2018

### metastable

Are both of these (seemingly contradictory) statements true in the same context:

“A free electron can absorb and also re-emit a photon in less time than it takes for the photon to traverse its wave-length in a vacuum (wavelength meters/c), such as in the process of compton scattering or inverse compton scattering.”

“Information cannot travel faster than the speed of light in a vacuum”

Last edited: Dec 7, 2018
14. Dec 7, 2018

### Staff: Mentor

The second is true, the first is ill-defined.

As there is no point in repeating the same question and answer over and over again I closed this thread.