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Thermal Doppler Broadening of Frequency

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 frequency.

Formula

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

symbol description physical quantity
σf standard deviation "Frequency"
m mass of a particle "Mass"
T temperature "Temperature"
fs frequency at the source "Frequency"
ΔfFWHM frequency full width at half-maximum "Frequency"

Forms

Examples

Get the resource:

In[1]:=
ResourceObject["Thermal Doppler Broadening of Frequency"]
Out[1]=

Get the formula:

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

In[3]:=
FormulaData[ ResourceObject[ "Thermal Doppler Broadening of Frequency"], {QuantityVariable[ Row[{"\[CapitalDelta]", \!\(\*SubscriptBox[\("f"\), \("FWHM"\)]\)}],"Frequency"] -> Quantity[6.535`, "Gigahertz"], QuantityVariable[ \!\(\*SubscriptBox[\("f"\), \("s"\)]\),"Frequency"] -> Quantity[745, "Terahertz"]}]
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