Finding The Spectral Line Width

In summary, to determine the line width of the spectral line representing the 5 to 2 transition in hydrogen, one can use the uncertainty principle and the given data of the lifetimes of n = 5 and n = 2. The equation for delta E can be used to calculate the line width, with the notation of h or hbar taken into consideration.
  • #1
Dew.J
6
0
[STRIKE][STRIKE][/STRIKE][/STRIKE]

Homework Statement



Using only the information above (previous problem), what is the line width of the spectral line representing the 5 to 2 transition in H (hydrogen)

Homework Equations


Given Data: lifetime of n = 5 is 7.52ns
lifetime of n = 2 is 1.38ns
Thus, total t = 8.9ns

delta E = h/delta T = 4.63x10-7 eV


The Attempt at a Solution



looking through the book I find that Delta X (width of the wave packet) = h/p where p = SQRT(2*Me*E). However, i can find no equation that expressly relates the width of the spectral line. Is this Delta X what I am looking for or is their another equation that I'm not seeing. Thanks.
 
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  • #2
Hi,
I guess your delta E = h/delta T = 4.63x10-7 eV can be correct!
Or better:
Use the uncertainty principle that related spread of energy and life time! Also take care of notations like h or hbar.
 

FAQ: Finding The Spectral Line Width

What is spectral line width?

Spectral line width refers to the measurement of the width of a spectral line in a spectrum. It is usually measured in units of frequency or wavelength and can give information about the properties of the source emitting the spectrum.

Why is finding the spectral line width important?

Finding the spectral line width is important because it can provide valuable information about the physical processes and properties of the emitting source. It can also help identify the type of object emitting the spectrum and its motion relative to the observer.

How is the spectral line width measured?

The spectral line width can be measured using various techniques such as fitting a Gaussian curve to the spectral line, calculating the full width at half maximum (FWHM), or using Fourier analysis. The specific method used depends on the type of spectrum and the desired level of precision.

What factors can affect the spectral line width?

The spectral line width can be affected by several factors including the temperature, pressure, and density of the emitting source. It can also be influenced by the source's motion, magnetic fields, and other physical conditions. Instrumental effects and observational errors can also contribute to the measured line width.

How does the spectral line width relate to other properties of the emitting source?

The spectral line width is closely related to the energy and velocity of the particles emitting the spectrum. It can also provide information about the temperature, turbulence, and other physical conditions of the source. By studying the spectral line width, scientists can gain insights into the structure and dynamics of objects such as stars, galaxies, and interstellar gas clouds.

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