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ATM-14

Hydrogen 21-cm hyperfine

ν = 1420.4 MHz, λ = c/ν ≈ 21.1 cm. The I·J splitting of hydrogen 1s.

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SpectraHyperfine

Governing equation

ν=1420.405 MHz,λ=c/ν\nu=1420.405\,\mathrm{MHz},\quad\lambda=c/\nu

s∈[0.5,2]s \in \left[0.5, 2\right]

where

s
Scale vs H (—)
\nu
Frequency (MHz)
\lambda
Wavelength (cm)

The figure, part by part

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ATM-14 · spectrum
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①

Governing law — red

ν=1420.405 MHz,λ=c/ν\nu=1420.405\,\mathrm{MHz},\quad\lambda=c/\nu

s∈[0.5,2]s \in \left[0.5, 2\right]

s=0.5s = 0.5ν=42.21\nu = 42.21

②

Domain of the variable — blue

smin⁡=0.5,smax⁡=2s_{\min} = 0.5,\quad s_{\max} = 2

s∈[0.5,2]s \in \left[0.5, 2\right]

s=0.5s = 0.5s=0.5s = 0.5

③

Response curve — green

ν=1420.405 MHz,λ=c/ν\nu=1420.405\,\mathrm{MHz},\quad\lambda=c/\nu

s∈[0.5,2]s \in \left[0.5, 2\right]

s=0.5s = 0.5ν=42.21\nu = 42.21

④

Rate of change — amber

dνds\frac{\mathrm{d}\nu}{\mathrm{d}s}

s∈[0.5,2]s \in \left[0.5, 2\right]

s=0.509s = 0.509ν′=−81.35\nu^{\prime} = -81.35

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-14 — Hydrogen 21-cm hyperfine) is the form associated with Hyperfine. Working symbols: ss →\rightarrow ν\nu, λ\lambda. The line maps neutral hydrogen across the Galaxy. A pedagogical scaler lets you detune ν.

Purpose

Purpose: compute ν\nu, λ\lambda from ss in Atomic physics via ν=1420.405 MHz,λ=c/ν\nu=1420.405\,\mathrm{MHz},\quad\lambda=c/\nu ν = 1420.4 MHz, λ = c/ν ≈ 21.1 cm. The I·J splitting of hydrogen 1s. 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 s=1.000 —s = 1.000\,\mathrm{—}, the governing relation ν=1420.405 MHz,λ=c/ν\nu=1420.405\,\mathrm{MHz},\quad\lambda=c/\nu yields ν=1420.406 MHz\nu = 1420.406\,\mathrm{MHz}, λ=21.106 cm\lambda = 21.106\,\mathrm{cm}. A spin-flip, a 21 cm wave. Move a slider: the numbers are this situation, not a canned story.

Calculator

Inputs

Outputs

  • Frequency \nu1420.406 MHz
  • Wavelength \lambda21.106 cm
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ATM-14 · spectrum
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Narration of this film

A spin-flip, a 21 cm wave.

The line maps neutral hydrogen across the Galaxy. A pedagogical scaler lets you detune ν.

Reading speed

Watch on YouTube