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Index/Atomic physics/ATM-22

ATM-22

Linear Stark snapshot

ΔE = e E ⟨z⟩. First-order Stark shift of a permanent electric dipole.

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Governing equation

ΔE=eE⟨z⟩\Delta E=e\mathcal{E}\langle z\rangle

E∈[0.1,200]\mathcal{E} \in \left[0.1, 200\right]

where

\mathcal{E}
Electric field (kV/cm)
\langle z\rangle
Dipole length (Å)
\Delta E
Stark shift (meV)

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ATM-22 · spectrum
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①

Governing law — red

ΔE=eE⟨z⟩\Delta E=e\mathcal{E}\langle z\rangle

E∈[0.1,200]\mathcal{E} \in \left[0.1, 200\right]

E=0.1\mathcal{E} = 0.1ΔE=0.003\Delta E = 0.003

②

Domain of the variable — blue

Emin⁡=0.1,Emax⁡=200\mathcal{E}_{\min} = 0.1,\quad \mathcal{E}_{\max} = 200

E∈[0.1,200]\mathcal{E} \in \left[0.1, 200\right]

E=0.1\mathcal{E} = 0.1E=0.1\mathcal{E} = 0.1

③

Response curve — green

ΔE=eE⟨z⟩\Delta E=e\mathcal{E}\langle z\rangle

E∈[0.1,200]\mathcal{E} \in \left[0.1, 200\right]

E=0.1\mathcal{E} = 0.1ΔE=0.003\Delta E = 0.003

④

Rate of change — amber

dΔEdE\frac{\mathrm{d}\Delta E}{\mathrm{d}\mathcal{E}}

E∈[0.1,200]\mathcal{E} \in \left[0.1, 200\right]

E=1.357\mathcal{E} = 1.357ΔE′=0.03\Delta E^{\prime} = 0.03

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-22 — Linear Stark snapshot) is the form associated with Stark. Working symbols: E\mathcal{E}, ⟨z⟩\langle z\rangle →\rightarrow ΔE\Delta E. Hydrogen n=2 is linear because of ℓ degeneracy. Most atoms start at second order (polarizability).

Purpose

Purpose: compute ΔE\Delta E from E\mathcal{E}, ⟨z⟩\langle z\rangle in Atomic physics via ΔE=eE⟨z⟩\Delta E=e\mathcal{E}\langle z\rangle ΔE = e E ⟨z⟩. First-order Stark shift of a permanent electric dipole. 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 E=10.000 kV/cm\mathcal{E} = 10.000\,\mathrm{kV/cm}, ⟨z⟩=3.000 A˚\langle z\rangle = 3.000\,\mathrm{Å}, the governing relation ΔE=eE⟨z⟩\Delta E=e\mathcal{E}\langle z\rangle yields ΔE=0.300 meV\Delta E = 0.300\,\mathrm{meV}. An atom, a static E, a shifted line. Move a slider: the numbers are this situation, not a canned story.

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Outputs

  • Stark shift \Delta E0.300 meV
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ATM-22 · spectrum
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Narration of this film

An atom, a static E, a shifted line.

Hydrogen n=2 is linear because of ℓ degeneracy. Most atoms start at second order (polarizability).

Reading speed

Watch on YouTube