ATM-33

Doppler width

Thermal broadening.

Reading speed

AtomicDoppler

Governing equation

\Delta\nu/\nu=\sqrt{2kT\ln2/mc^2}

$T \in \left[100, 20000\right]$

where

T: T (K)
m: Mass (u)
\Delta\nu/\nu: Fraction (—)

The figure, part by part

Each numbered marker wears the color of its card. Hover a card to light the marker. Tap a marker to jump to that card. The slider walks a red point along the curve; Animate drawing traces it like a pen.

00:0 / 00:08

①

Governing law — red

\Delta\nu/\nu=\sqrt{2kT\ln2/mc^2}

$T \in \left[100, 20000\right]$

$T = 100$ $\Delta\nu/\nu = 3.58\times 10^{-6}$

Along the curve

②

Domain of the variable — blue

T_{\min} = 100,\quad T_{\max} = 20000

$T \in \left[100, 20000\right]$

$T = 100$ $T = 100$

Along the curve

③

Response curve — green

\Delta\nu/\nu=\sqrt{2kT\ln2/mc^2}

$T \in \left[100, 20000\right]$

$T = 100$ $\Delta\nu/\nu = 3.58\times 10^{-6}$

Along the curve

④

Rate of change — amber

\frac{\mathrm{d}\Delta\nu/\nu}{\mathrm{d}T}

$T \in \left[100, 20000\right]$

$T = 225.2$ $\Delta\nu/\nu^{\prime} = 1.25\times 10^{-8}$

Along the curve

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-33 — Doppler width) is the form associated with Doppler. Working symbols: $T$ , $m$ $\rightarrow$ $\Delta\nu/\nu$ . Thermal broadening.

Purpose

Purpose: compute

\Delta\nu/\nu

from

T

m

in Atomic physics via

\Delta\nu/\nu=\sqrt{2kT\ln2/mc^2}

Thermal broadening. 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

T = 5000.000\,\mathrm{K}

m = 1.000\,\mathrm{u}

, the governing relation

\Delta\nu/\nu=\sqrt{2kT\ln2/mc^2}

yields

\Delta\nu/\nu = 2.532e-5\,\mathrm{—}

. Thermal broadening. Move a slider: the numbers are this situation, not a canned story.

Calculator

Inputs

T T5000 KMass m1 u

Outputs

Fraction \Delta\nu/\nu0.00002532 —

Reading speed

Watch on YouTube

Free library

Full library

Free PDF / open book

YouTube channels

00:0 / 00:08

Narration of this film

Thermal broadening.

Reading speed

Watch on YouTube