ATM-06

Stern–Gerlach force

F_z = μ_z dB/dz, μ_z = − g μ_B m_s. Beam split by a field gradient.

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StructureStern–Gerlach

Governing equation

F_z=-g\mu_B m_s\,dB/dz

$dB/dz \in \left[0.1, 200\right]$

where

g: g-factor (—)
m_s: m_s (—)
dB/dz: Gradient (T/m)
F_z: Force (zN)

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

F_z=-g\mu_B m_s\,dB/dz

$dB/dz \in \left[0.1, 200\right]$

$dB/dz = 0.1$ $F_z = -9.27\times 10^{-4}$

Along the curve

②

Domain of the variable — blue

dB/dz_{\min} = 0.1,\quad dB/dz_{\max} = 200

$dB/dz \in \left[0.1, 200\right]$

$dB/dz = 0.1$ $dB/dz = 0.1$

Along the curve

③

Response curve — green

F_z=-g\mu_B m_s\,dB/dz

$dB/dz \in \left[0.1, 200\right]$

$dB/dz = 0.1$ $F_z = -9.27\times 10^{-4}$

Along the curve

④

Rate of change — amber

\frac{\mathrm{d}F_z}{\mathrm{d}dB/dz}

$dB/dz \in \left[0.1, 200\right]$

$dB/dz = 1.357$ $F_z^{\prime} = -0.009$

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-06 — Stern–Gerlach force) is the form associated with Stern–Gerlach. Working symbols: $g$ , $m_s$ , $dB/dz$ $\rightarrow$ $F_z$ . Silver atoms, two spots: the discovery of space quantisation. Spin ½ has m_s = ±1/2.

Purpose

Purpose: compute

F_z

from

g

m_s

dB/dz

in Atomic physics via

F_z=-g\mu_B m_s\,dB/dz

F_z = μ_z dB/dz, μ_z = − g μ_B m_s. Beam split by a field gradient. 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

g = 2.000\,\mathrm{—}

m_s = 0.500\,\mathrm{—}

dB/dz = 10.000\,\mathrm{T/m}

, the governing relation

F_z=-g\mu_B m_s\,dB/dz

yields

F_z = -0.093\,\mathrm{zN}

. An oven, a magnet, two spots on a plate. Move a slider: the numbers are this situation, not a canned story.

Calculator

Inputs

g-factor g2 —m_s m_s0.5 —Gradient dB/dz10 T/m

Outputs

Force F_z-0.093 zN

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Narration of this film

An oven, a magnet, two spots on a plate.

Silver atoms, two spots: the discovery of space quantisation. Spin ½ has m_s = ±1/2.

Reading speed

Watch on YouTube