Effective Transverse Relaxation Time Calculator

Formula Used:

\[ T2' = \frac{1}{\pi \times \Delta\nu_{1/2}} \]

Effective Transverse Relaxation Time (T2'):

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1. What is Effective Transverse Relaxation Time?

Effective Transverse Relaxation Time (T2'), also known as dephasing time, is a combination of transverse relaxation and magnetic field inhomogeneity. It represents the time constant for the decay of transverse magnetization in NMR spectroscopy.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ T2' = \frac{1}{\pi \times \Delta\nu_{1/2}} \]

Where:

\( T2' \) — Effective Transverse Relaxation Time (seconds)
\( \pi \) — Archimedes' constant (approximately 3.14159)
\( \Delta\nu_{1/2} \) — Observed Width at Half-Height (1/second)

Explanation: This formula calculates the effective transverse relaxation time from the phenomenological linewidth of the resonance lineshape, which is a primary factor affecting both resolution and signal-to-noise ratio of NMR spectra.

3. Importance of T2' Calculation

Details: Accurate T2' estimation is crucial for understanding spin-spin relaxation processes, optimizing NMR pulse sequences, and interpreting spectral line shapes in magnetic resonance experiments.

4. Using the Calculator

Tips: Enter the observed width at half-height in units of 1/second. The value must be positive and non-zero for accurate calculation.

5. Frequently Asked Questions (FAQ)

Q1: What is the difference between T2 and T2'?
A: T2 represents the intrinsic transverse relaxation time, while T2' includes both intrinsic relaxation and external field inhomogeneity effects.

Q2: How does field inhomogeneity affect T2'?
A: Magnetic field inhomogeneity causes additional dephasing of spins, leading to a shorter effective transverse relaxation time (T2') compared to the intrinsic T2.

Q3: What are typical values for T2'?
A: T2' values vary widely depending on the sample and magnetic field strength, typically ranging from milliseconds to seconds in biological tissues.

Q4: How can T2' be measured experimentally?
A: T2' can be measured using various NMR pulse sequences such as gradient echo sequences or by analyzing the linewidth of NMR spectra.

Q5: Why is π used in the formula?
A: The factor of π comes from the relationship between the full width at half maximum of a Lorentzian lineshape and the relaxation time constant.