Expressing the full width at half maximum Δω by τ

In summary, the FWHM is a measure of the width of a peak or curve at its half maximum height and is commonly used in scientific research. It is directly related to the decay time constant (τ) and expressing it in terms of τ allows for a better understanding and comparison of different peaks. The FWHM can be measured by finding the points where the intensity is half of the maximum value, but it is not a measure of accuracy and should be interpreted in the context of other factors.
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Homework Statement



I need to express the full width at half maximum Δω as an expression in terms of τ.

Homework Equations



I'm guessing that the expression of Δω will fulfill this task.

The Attempt at a Solution



The problem is I have no idea how to go about the calculations :|
 
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1. What is the significance of expressing the full width at half maximum (FWHM)?

The FWHM is a measure of the width of a peak or curve at its half maximum height. It is commonly used in scientific research to describe the width of spectral lines, absorption bands, or other types of peaks. It provides important information about the shape and characteristics of a peak.

2. How is the FWHM related to the decay time constant (τ)?

The FWHM is directly related to the decay time constant (τ) through the equation Δω = 2/τ, where Δω represents the FWHM. This relationship is often used in spectroscopy to determine the decay rates of excited states or the lifetimes of molecules.

3. Why is it important to express the FWHM in terms of the time constant (τ)?

Expressing the FWHM in terms of the time constant (τ) allows for a better understanding of the physical processes underlying the observed peak. It also allows for easier comparison between different peaks or curves, even if they have different shapes or amplitudes.

4. How is the FWHM measured in experimental data?

The FWHM can be measured by finding the points on either side of the peak where the intensity is half of the maximum value. The distance between these two points corresponds to the FWHM. This measurement can be done manually or using software programs that have built-in FWHM analysis tools.

5. Can the FWHM be used to determine the accuracy of a measurement?

No, the FWHM is not a measure of accuracy. It only describes the width of a peak or curve at its half maximum height. Other factors, such as signal-to-noise ratio and instrument resolution, also play a role in the accuracy of a measurement. The FWHM should be interpreted in the context of these other factors.

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