[halfaxa]

Hello,

I was wondering if anyone could help me with a question that was given in a recent tutorial but was not covered in the answer session. The question concerns the T₂relaxation time constant and the spin echo technique. Basically the question requires you to work out the T₂ relaxation time constant for an NMR peak whose intensity measured with 2t = 50 ms is 60% of that measured at 2t = 0 ms in the spin echo sequence.

I am pretty sure you have to use the following equation:

I(2t) = I(0)exp(-2t/T₂)

where I is intensity.

However I am not sure if I am going about the question in the right way, though my problems may be purely mathematical rather than chemical! I'll give an overview of my working out and hopefully someone can tell me where/if I'm going wrong.

Calculation

Since the intensity of the NMR signal after 2t = 50ms is 60% of that when 2t = 0 I substituted in 0.6 in place of I(2t) and 1 in place of I(0):

0.6 = exp(-2t/T₂)

I then took logarithms of either side and rearrange to get:

-0.511T₂ = -2t

Then I convert 50 ms to seconds i.e 0.05 s and substitute it in and rearrange to finally get:

T₂ = 0.098

Firstly, I am doubting my maths here, having not done a proper maths course in about 6 years I don't even know if my approach is ok. Secondly, I don't really understand the nature of the T₂ relaxation constant and so I don't know what the units are etc. This means I don't know whether I should even have converted from ms to seconds at the last step.

I would really appreciate any help as the question appears to come up quite often in exams so it would be good to properly understand how to tackle such a question.

[dipesh747]