Stern-Gerlach Deflection Calculator

Stern-Gerlach Deflection Calculator | Online Free Tool | Elysia Tools

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

1Enter the magnetic field gradient (dB/dz), magnet length, particle velocity, drift distance, magnetic moment, and atomic mass.
2The tool computes transverse acceleration inside the magnet using a = μ_z · (dB/dz) / m.
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).

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

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

Key facts

Overview

When to use

How it works

Use cases

Examples

1. Standard Silver Beam Demonstration

2. Thermal Velocity Increase Analysis

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