ATM-17

Doppler line width

Δν_D = (ν₀ / c) √(2 k T / m). FWHM is 2√(ln 2) times this 1/e half-width.

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SpectraDoppler width

Governing equation

\Delta\nu_D=(\nu_0/c)\sqrt{2kT/m}

where

\nu_0: Line frequency (THz)
T: Temperature (K)
M: Mass (u)
\Delta\nu_D: 1/e half-width (GHz)
\mathrm{FWHM}: FWHM (GHz)

Lecture brief

Historical brief

Balmer, Rydberg, Bohr (1913), fine structure, Zeeman and Stern–Gerlach built the spectrum of one atom. The lab computes levels, selection and magnetic splitting. This sheet (ATM-17 — Doppler line width) is the form associated with Doppler width. Working symbols: $\nu_0$ , $T$ , $M$ $\rightarrow$ $\Delta\nu_D$ , $\mathrm{FWHM}$ . The dominant broadening in hot, low-density gas. Turbulence adds in quadrature.

Purpose

Purpose: compute

\Delta\nu_D

\mathrm{FWHM}

from

\nu_0

T

M

in Atomic physics via

\Delta\nu_D=(\nu_0/c)\sqrt{2kT/m}

Δν_D = (ν₀ / c) √(2 k T / m). FWHM is 2√(ln 2) times this 1/e half-width. Use it when a real atomic physics question must be answered in SI before a code check.

Live realistic example

In symbols

Live case. Given

\nu_0 = 455.000\,\mathrm{THz}

T = 5000.000\,\mathrm{K}

M = 1.000\,\mathrm{u}

, the governing relation

\Delta\nu_D=(\nu_0/c)\sqrt{2kT/m}

yields

\Delta\nu_D = 13.839\,\mathrm{GHz}

\mathrm{FWHM} = 23.044\,\mathrm{GHz}

. A thermal cloud, a Gaussian line. Move a slider: the numbers are this situation, not a canned story.

Calculator

Inputs

Line frequency \nu_0455 THzTemperature T5000 KMass M1 u

Outputs

1/e half-width \Delta\nu_D13.839 GHz
FWHM \mathrm{FWHM}23.044 GHz

Reading speed

Watch on YouTube

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Narration of this film

A thermal cloud, a Gaussian line.

The dominant broadening in hot, low-density gas. Turbulence adds in quadrature.

Reading speed

Watch on YouTube