ATM-13

Lamb-shift snapshot

ΔE ≈ 1057 (Z/1)⁴ (2/n)³ MHz for the 2S–2P hydrogenic sketch.

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StructureLamb

Governing equation

\Delta E_{\mathrm{Lamb}}\approx 1057\,Z^4(2/n)^3\,\mathrm{MHz}

$Z \in \left[1, 10\right]$

where

Z: Atomic number (—)
n: n (—)
\Delta\nu: Lamb shift (MHz)

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.

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①

Governing law — red

\Delta E_{\mathrm{Lamb}}\approx 1057\,Z^4(2/n)^3\,\mathrm{MHz}

$Z \in \left[1, 10\right]$

$Z = 1$ $\Delta\nu = 1057.8$

Along the curve

②

Domain of the variable — blue

Z_{\min} = 1,\quad Z_{\max} = 10

$Z \in \left[1, 10\right]$

$Z = 1$ $Z = 1$

Along the curve

③

Response curve — green

\Delta E_{\mathrm{Lamb}}\approx 1057\,Z^4(2/n)^3\,\mathrm{MHz}

$Z \in \left[1, 10\right]$

$Z = 1$ $\Delta\nu = 1057.8$

Along the curve

④

Rate of change — amber

\frac{\mathrm{d}\Delta\nu}{\mathrm{d}Z}

$Z \in \left[1, 10\right]$

$Z = 1.057$ $\Delta\nu^{\prime} = 5005.7$

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-13 — Lamb-shift snapshot) is the form associated with Lamb. Working symbols: $Z$ , $n$ $\rightarrow$ $\Delta\nu$ . QED vacuum fluctuations split 2S_{1/2} from 2P_{1/2}. Dirac had left them degenerate.

Purpose

Purpose: compute

\Delta\nu

from

Z

n

in Atomic physics via

\Delta E_{\mathrm{Lamb}}\approx 1057\,Z^4(2/n)^3\,\mathrm{MHz}

ΔE ≈ 1057 (Z/1)⁴ (2/n)³ MHz for the 2S–2P hydrogenic sketch. 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

Z = 1.000\,\mathrm{—}

n = 2.000\,\mathrm{—}

, the governing relation

\Delta E_{\mathrm{Lamb}}\approx 1057\,Z^4(2/n)^3\,\mathrm{MHz}

yields

\Delta\nu = 1057.85\,\mathrm{MHz}

. Two nearly coincident levels, a tiny QED gap. Move a slider: the numbers are this situation, not a canned story.

Calculator

Inputs

Atomic number Z1 —n n2 —

Outputs

Lamb shift \Delta\nu1057.85 MHz

Reading speed

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Narration of this film

Two nearly coincident levels, a tiny QED gap.

QED vacuum fluctuations split 2S_{1/2} from 2P_{1/2}. Dirac had left them degenerate.

Reading speed

Watch on YouTube