How many periods of a photon are involved in proton energy level transistion?

[fred1234]

In MR there is the resonance condition that for a proton in a lower energy state, a photon with a frequency that matches the energy separation between states, E=hf, can transmission the proton to the higher energy state by absorbing said photon.

The question then is how long does this interaction take? How long does it take for the proton to establish that the frequency has matched?
a) a fraction of a period (1/f).
b) a period.
c) multiple periods.

Assume all other conditions, i.e. proximity, direction, etc, are matched.

Thanks,

Fred

[LostConjugate]

I think there is a probability that it will happen every \frac{h}{E} seconds?

Edit:

From an example of finding the time evolution of the system, it looks like its more complicated then a simple answer, looks like you need the equations to find the time it takes, good question though.

[Bill_K]

Fred1234, you're trying to ask classical questions about a quantum system. The photon does not get gradually absorbed, it interacts with the proton all at once. Exactly when this happens has a spread in probability.

It's easier to consider the inverse process, in which the excited proton emits a photon. The state has some average lifetime, say Δt. This value determines the energy spread of the photon, and hence the length of the wavepacket emitted. At the same time the photon has energy E, corresponding to a frequency ω = E/h and a period t = 2π/ω. But there is no relationship between t and Δt, which is what you're trying to ask.

[fred1234]

A magnetic field, that is experienced by a proton(a spin in MR lingo), is oscillating at a frequency \omega which is near but not exactly \omega_{0} the Lamar frequency of the spin, i.e. does not meet resonance condition. I then instantaneously alter the rate at which the magnetic field oscillates so that \omega=\omega_{0}. How long will it take the proton to recognizes that resonance has occurred? I am not so concerned with how long it takes to actually absorb (or emit) the photon.

In signal processing the Fourier Transform is used to recognize frequencies, which dictates at least a couple of periods of oscillation to recognize the frequency. I have yet to see a description of what actually transpires for the spin to recognize the frequency, so trying to guess at how long this process take is a mystery to me. If the process requires syncing, i.e. a little nudging per period that sums over multiple periods to eventually cross a threshold, then I would assume answer c. If all the nudging happens at strategic points within a single oscillation and all the energy needed is contained within one period, then I would assume answer b. If for some quantum mechanical reason time is not required to recognize frequency and the process is virtually instantaneous, then I would assume answer a.

Bill_K: is \Delta t the time in the excited state or the time to emit the photon.

If this is a probabilistic time period I would assume there is theory as to the mean and variance predicted.

Thanks,

Fred