The Spacetime Metric

Level 2 · Secondary physics teaching kit · Grades 10–12

Introductory nuclear physics and reaction evidence

Use the learner record during the live investigation, then use the instructor guide to facilitate comparison, address misconceptions, and assess evidence-bounded reasoning.

Learner lab record

Reaction yield and detector-efficiency audit

How do beam rate, target thickness, cross section, and detection efficiency combine into an expected count rate?

Setup

Use the reaction-yield laboratory. Begin in the thin-target regime, vary one factor at a time, and keep physical reaction yield separate from detector counts.

Predict first

  1. 1. Predict the yield response to doubling beam rate in the thin-target limit.
  2. 2. Predict what detector efficiency changes and what it leaves unchanged.
Variables
VariableRoleUnit
Beam particle rateindependentparticles/s
Target areal densityindependentnuclei/area
Reaction cross sectionmodel inputarea
Reaction and detected ratesdependentevents/s and counts/s

Observation columns

beam rateareal densitycross sectionreaction rateefficiencycount rate

Analyze

  1. 1. Which runs demonstrate linear scaling?
  2. 2. When would the thin-target approximation fail?
  3. 3. Why are counts not automatically proof of the proposed reaction channel?
  4. 4. Name two background or calibration controls.

Conclusion frame

Changing ___ by a factor of ___ changed modeled reaction rate by ___; detection efficiency changed ___ but not ___.

Instructor guide · 50–60 minutes

Teach the investigation, not the interface

Learning target: Learners construct a reaction-yield ledger and separate modeled physical events from detector acceptance, backgrounds, and identification.

Prepare

  • Review scientific notation and area units.
  • State the thin-target approximation.
  • Prepare one background-only and one calibration run.

Facilitation moves

  • Ask what happens in the target before what appears in the detector.
  • Require dimensional checks.
  • Keep channel identification separate from total count excess.

Accessibility and participation

  • Translate powers of ten into factor language.
  • Use a flow diagram from beam to target to detector.
  • Provide unit cards and calculator support.

Evidence of learning

  • A dimensionally consistent yield ledger
  • Correct efficiency separation
  • A credible background-control plan

Misconception checks

Every detector count is a nuclear reaction.

Counts include backgrounds and acceptance effects; channel identification requires calibrated signatures and controls.

Cross section is the physical size of a nucleus.

It is an interaction-probability measure with area units, not usually a geometric silhouette.

Extension

Add target attenuation and compare the exact thick-target expression with the linear approximation.