0 An accurate measurement of the fundamental spin-spin relaxation time (T2) come

Question

0 An accurate measurement of the fundamental spin-spin relaxation time (T2) comes from the amplitude of the "spin echo" as a function of delay time (T). The experiment involves a 900 pulse that rotates the spins into the x-y plane, where they precess at a range of frequencies due to the range of local fields. After the delay time T, a 180° pulse is applied so that the spins that were ahead by precessing faster are inverted to become behind the spins that precessed slower. A large-amplitude spin echo occurs at an additional delay of T, when the faster precessing spins temporarily coincide with the slower precessing spins. Question 1 2 pts When the delay time between the 900 and 1800 pulses is T-5.66 ms, the spin echo (that occurs at a later time) becomes 1/e of its initial amplitude. The resulting spin-spin relaxation time is T2 D Question 2 2 pts The table (pasted below) gives the amplitudes of the spin echo as a function of the delay time between 90° and 180° pulses. Fitting the data to an exponential r delay(ms) 0.2 0.5 EcholV) 4024 3.786 3.364 2.791 2.239 1.868 1.725 1.152 0.838 0.462 7.5 10 15 elaxation function yields a spin-spin relaxation time of Ta ms

Explanation / Answer

Specifically, I have read: if there is a 90 degree rf pulse along y, then after some transverse dephasing has occurred, at a time "t", a second rf pulse is applied along y, then one gets a spin echo.

I understand that those spins that are aligned exactly along +y and -y at time t will refocus at time 2t to give an echo. But, I don't understand how any other spins can contribute to such an echo.

For example:

If a spin is at the pi/4 angle between the +x and +y axes at time "t" and another spin is between the +x and -y axes at time "t" then following the second 90 degree rf pulse, as far as the xy plane is concerned, the spins are now along +y and -y respectively. So at 2t, the spins have each rotated only pi/4 towards each other, so they are not refocused. So when spins that were initially along +y and -y refocus, these other spins will not have refocused yet. That is, the spins are not refocussing together. So how do we get an echo? This doesn't appear similar to the spin echo following a 90-180, where the spins all come back into focus at the same point in time.

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