# Stern-Gerlach Deflection Calculator

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.

> Canonical page: https://elysiatools.com/en/tools/stern-gerlach-deflection

- **Category:** Science & Education

- **Keywords:** stern gerlach, space quantization, spin measurement, magnetic moment, beam splitting, quantum mechanics

## 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.

## Inputs

- **Field gradient dB/dz (T/m)** (number): e.g. 1000
- **Magnet length L (cm)** (number): e.g. 3.5
- **Atom velocity v (m/s)** (number): e.g. 500
- **Drift distance D (cm)** (number): e.g. 20
- **Magnetic moment |μ| (μB)** (number): e.g. 1
- **Atom mass (u)** (number): e.g. 107.8682

## 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

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

## Frequently asked questions

### 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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