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Stern-Gerlach Deflection Calculator

· Last updated：2026-08-29

a = μ_z·G/m, deflection z = a·[(L/v)²/2 + L·D/v²], and 2z screen separation for spin-1/2 atoms in a field gradient.

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Tool usage guide

Learn when to use this tool, what it supports, and how real users apply it.

Key facts

Category
Science & Education
Input types
number
Output type
text
Sample coverage
4
API ready
Yes

Overview

The Stern-Gerlach Deflection Calculator computes the transverse acceleration, individual beam deflection, and total screen separation for spin-1/2 neutral particles traversing an inhomogeneous magnetic field gradient.

When to use

  • Predicting beam displacement and spot separation when modeling quantum spin-selection apparatuses.
  • Designing atomic beam experiments requiring specific magnetic field gradients and drift lengths.
  • Validating physics homework and lecture demonstrations involving space quantization and magnetic dipole moments.

How it works

  1. 1Enter the magnetic field gradient (dB/dz), magnet length, particle velocity, drift distance, magnetic moment, and atomic mass.
  2. 2The tool computes transverse acceleration inside the magnet using a = μ_z · (dB/dz) / m.
  3. 3It evaluates individual beam deflection using z = a · [(L/v)² / 2 + L · D / v²] and doubles the result to determine total beam separation on the detection plane.

Use cases

  • Reproducing classical Stern-Gerlach silver atom experiments to compare theoretical spot separation with experimental plates.
  • Optimizing furnace temperature and velocity selectors to ensure resolvable beam separation.
  • Calculating magnetic force and trajectory deviations for alkali metal beams in atomic physics research.

Examples

1. Standard Silver Beam Demonstration

Physics Educator

Background

An instructor is preparing a lecture on space quantization and wants to demonstrate standard historical experimental values.

Problem

Calculate the expected separation between spin-up and spin-down silver atom spots on the detector screen.

How to use

Set gradient to 1000 T/m, magnet length to 3.5 cm, velocity to 500 m/s, drift distance to 20 cm, magnetic moment to 1 μB, and atomic mass to 107.8682 u.

Field gradient dB/dz: 1000 T/m, Magnet length L: 3.5 cm, Velocity v: 500 m/s, Drift distance D: 20 cm, Magnetic moment |μ|: 1 μB, Atom mass: 107.8682 u

Outcome

Yields an acceleration of 5.178 × 10⁴ m/s², an individual deflection of 1.577 mm, and a total beam separation of 3.153 mm.

2. Thermal Velocity Increase Analysis

Atomic Physics Student

Background

A student is analyzing how higher oven temperatures affect beam collimation and spot resolution.

Problem

Determine the spot separation when thermal velocity is doubled to 1000 m/s.

How to use

FAQ

What formula calculates the deflection inside and outside the magnet?

Deflection is calculated as z = a · [(L/v)² / 2 + L · D / v²], combining parabolic motion inside the magnet with linear drift after exiting.

How does particle velocity affect beam deflection?

Deflection is inversely proportional to the square of velocity (1/v²), so doubling the velocity reduces deflection to approximately one quarter.

What units are required for the magnetic moment input?

The magnetic moment |μ| is entered in Bohr magnetons (μB).

Why does the beam split into two discrete spots?

Spin-1/2 atoms possess quantized magnetic moment projections of μ_z = +μ and μ_z = -μ, causing equal and opposite deflections.

What atomic mass units does the calculator expect?

The atomic mass is entered in unified atomic mass units (u, where 1 u ≈ 1.66054 × 10⁻²⁷ kg).

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Keep field parameters identical but increase velocity from 500 m/s to 1000 m/s.

Field gradient dB/dz: 1000 T/m, Magnet length L: 3.5 cm, Velocity v: 1000 m/s, Drift distance D: 20 cm, Magnetic moment |μ|: 1 μB, Atom mass: 107.8682 u

Outcome

Calculates an individual deflection of 0.394 mm and a total screen split of 0.788 mm, demonstrating the 1/v² scaling relationship.