Print broadening

The pressure broadening , also known as collision broadening referred to is a physical effect that the light spectrum influenced of a substance. ${\displaystyle \Delta \lambda _{p}}$

Overview

In theory, transitions between the different discrete energy levels of a molecule lead to the emission or absorption of photons of a very specific energy , i.e. a specific wavelength . As a result, the light spectrum would only consist of a few discrete lines .

In a real spectrum, however, not only a single wavelength is measured for each transition , but always a group of wavelengths around the actual transition, which is also referred to as “spectral uncertainty ”. In addition to the natural line width and the Doppler broadening , the print broadening is also a cause for this. It describes that part of the spectral uncertainty that arises due to the interaction with other atoms . ${\displaystyle \lambda }$

The pressure broadening is only relevant for lines with a narrow natural line width, i.e. a time-extended radiation or absorption process. If during this transition the molecule interacts with another particle through a collision , there is a brief frequency change. This has the effect that the phase of the oscillation after the collision no longer matches the phase before the collision. At high pressure there are many shocks, then the frequency sharpness is no longer determined by the duration of the radiation process, but by the mean time between two shocks.

This simple description only applies to short-range interactions between particles. The statistical distribution of the impacts then leads to a Lorentz profile , in combination with the Doppler broadening to a Voigt profile . In the case of long-range interactions, on the other hand, deviations can be observed: in particular, due to the mere presence of neighbors, there is a static pressure broadening that - unlike the collision broadening - does not increase with temperature.

appraisal

The pressure broadening can be estimated with the average time between collisions, which is a good approximation equal to the mean free path (for a simple gas) between two collisions, divided by the average velocity of the atoms: ${\displaystyle \Delta t}$ ${\displaystyle l}$ ${\displaystyle v}$

${\displaystyle \Delta t={\frac {l}{v}}={\frac {1}{n\sigma }}{\frac {1}{\sqrt {\frac {2k_{\mathrm {B} }T}{m}}}}}$

With

• the particle density , ${\displaystyle n}$
• the scattering cross-section ${\displaystyle \sigma }$
• the Boltzmann constant ${\displaystyle k_{\mathrm {B} }}$
• the temperature ${\displaystyle T}$
• the atomic mass . ${\displaystyle m}$

The line broadening then results in:

${\displaystyle \Rightarrow \Delta \lambda \approx {\frac {\lambda ^{2}}{\pi c\,\Delta t}}\approx {\frac {\lambda ^{2}}{\pi c}}n\sigma {\sqrt {\frac {2k_{\mathrm {B} }T}{m}}}}$

where is the speed of light . ${\displaystyle c}$

example

The pressure broadening of the Hα line ( ) in the sun results from ${\displaystyle \lambda =656{,}28\,\mathrm {nm} }$

• the mass of a hydrogen atom , ${\displaystyle m=1{,}7\cdot 10^{-27}\,\mathrm {kg} }$
• a particle number density , ${\displaystyle n\approx 1{,}5\cdot 10^{23}\,\mathrm {m} ^{-3}}$
• the scattering cross-section and ${\displaystyle \sigma \approx 10^{-21}\,\mathrm {m} ^{2}}$
• a temperature in the photosphere ${\displaystyle T\approx 5770\,\mathrm {K} }$

to about

${\displaystyle \Rightarrow \Delta \lambda _{p}\approx 6{,}6\cdot 10^{-7}\,\mathrm {nm} }$

It is thus far less than the natural line broadening of the Hα line of hydrogen and does not play a major role. ${\displaystyle (\Delta \lambda _{N}\approx 5\cdot 10^{-5}\,\mathrm {nm} )}$

literature

• Klaus Kleinermanns (editor) Bergmann, Schaefer Textbook of Experimental Physics , Volume 5 (gases, nanosystems, liquids), de Gruyter 2006, p. 325 (Uwe Riedel, Christof Schulz, Jürgen Warnatz, Jürgen Wolfrum, Chapter 3 Combustion ).