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Thermal Doppler Broadening of Wavelength

Doppler broadening is the broadening of spectral lines due to the Doppler effect, caused by a distribution of thermal velocities of atoms or molecules.

Doppler broadening increases with the square of the temperature, inversely with the square of the mass and directly with the source wavelength.

Formula

{QuantityVariable[Subscript["σ", "λ"], "Wavelength"] == Sqrt[(Quantity[1, "BoltzmannConstant"/"SpeedOfLight"^2]*QuantityVariable["T", "Temperature"])/QuantityVariable["m", "Mass"]]*QuantityVariable[Subscript["λ", "s"], "Wavelength"], QuantityVariable[Row[{"Δ", Subscript["λ", "FWHM"]}], "Wavelength"] == 2*Sqrt[2*Log[2]]*Sqrt[(Quantity[1, "BoltzmannConstant"/"SpeedOfLight"^2]*QuantityVariable["T", "Temperature"])/QuantityVariable["m", "Mass"]]*QuantityVariable[Subscript["λ", "s"], "Wavelength"]}

symbol description physical quantity
σλ standard deviation "Wavelength"
m mass of a particle "Mass"
T temperature "Temperature"
λs wavelength at the source "Wavelength"
ΔλFWHM wavelength full width at half-maximum "Wavelength"

Forms

Examples

Get the resource:

In[1]:=
ResourceObject["Thermal Doppler Broadening of Wavelength"]
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Get the formula:

In[2]:=
FormulaData[ ResourceObject["Thermal Doppler Broadening of Wavelength"]]
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Use some values:

In[3]:=
FormulaData[ ResourceObject[ "Thermal Doppler Broadening of Wavelength"], {QuantityVariable[ Row[{"\[CapitalDelta]", \!\(\*SubscriptBox[\("\[Lambda]"\), \("FWHM"\)]\)}],"Wavelength"] -> Quantity[3.53`, "Picometers"]}]
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