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## Spin-Up and Spin-Down Probabilities in the z-orientation: Instructor's Guide

*This activity can also be part of a larger integrated laboratory. See the Spins Lab 1 activity page.*

### Main Ideas

- Intrinsic Angular Momentum
- Quantization
- Magnetic Dipole Moment
- Quantum Probabilities

### Students' Task

*Estimated Time: 10 minutes*

Students must convince themselves that the probability a particle coming from the oven will be measured as either spin-up or spin-down in the z-direction is $\frac{1}{2}$.

### Prerequisite Knowledge

### Props/Equipment

- Tabletop Whiteboard with markers
- Computers with the Spins OSP software
- A handout for each student

### Activity: Introduction

This activity is best performed after having students Introduce Themselves to the Spins Program. Now that students have familiarized with how the program works, tell them that the next step is to make sure that the program itself effectively simulates the results of the Stern-Gerlach experiment. Ask them to fill out the handout provided using the software.

### Activity: Student Conversations

### Activity: Wrap-up

Ask to make sure the students are convinced the probability is one-half. Assure them this result is what much of the future analysis of the spin-$\frac{1}{2}$ system will be based upon.

### Extensions

This activity is the first part of SPINS Lab 1. It is designed to precede Probabilities for Different Spin-$\frac{1}{2}$ Stern Gerlach Analyzers and the Dice Rolling Lab.

The full lab is designed to be completed in a two hour lab block, while these individual activities are designed to be integrated into a normal lecture. We prefer to use the integrated activities, rather than the lab, but both are effective methods.