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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

where

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

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