ATM-21

Paschen–Back shift

ΔE = μ_B B (m_L + 2 m_S). Strong-field decoupling of L and S.

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SpectraPaschen–Back

Governing equation

\Delta E=\mu_B B(m_L+2m_S)

$B \in \left[0.5, 40\right]$

where

B: Field (T)
m_L: m_L (—)
m_S: m_S (—)
\Delta E: Shift (µeV)

The figure, part by part

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①

Governing law — red

\Delta E=\mu_B B(m_L+2m_S)

$B \in \left[0.5, 40\right]$

$B = 0.5$ $\Delta E = 57.88$

Along the curve

②

Domain of the variable — blue

B_{\min} = 0.5,\quad B_{\max} = 40

$B \in \left[0.5, 40\right]$

$B = 0.5$ $B = 0.5$

Along the curve

③

Response curve — green

\Delta E=\mu_B B(m_L+2m_S)

$B \in \left[0.5, 40\right]$

$B = 0.5$ $\Delta E = 57.88$

Along the curve

④

Rate of change — amber

\frac{\mathrm{d}\Delta E}{\mathrm{d}B}

$B \in \left[0.5, 40\right]$

$B = 0.748$ $\Delta E^{\prime} = 115.8$

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-21 — Paschen–Back shift) is the form associated with Paschen–Back. Working symbols: $B$ , $m_L$ , $m_S$ $\rightarrow$ $\Delta E$ . When μ_B B ≫ A, J is no longer good. The pattern reverts toward the normal Zeeman triplet.

Purpose

Purpose: compute

\Delta E

from

B

m_L

m_S

in Atomic physics via

\Delta E=\mu_B B(m_L+2m_S)

ΔE = μ_B B (m_L + 2 m_S). Strong-field decoupling of L and S. 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

B = 8.000\,\mathrm{T}

m_L = 1.000\,\mathrm{—}

m_S = 0.500\,\mathrm{—}

, the governing relation

\Delta E=\mu_B B(m_L+2m_S)

yields

\Delta E = 926.14\,\mathrm{\mu eV}

. A strong B, two independent projections. Move a slider: the numbers are this situation, not a canned story.

Calculator

Inputs

Field B8 Tm_L m_L1 —m_S m_S0.5 —

Outputs

Shift \Delta E926.14 µeV

Reading speed

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Narration of this film

A strong B, two independent projections.

When μ_B B ≫ A, J is no longer good. The pattern reverts toward the normal Zeeman triplet.

Reading speed

Watch on YouTube