Crystal Decay Lab Journal Crystal Decay Lab
Geologic Survey Investigation P.2.8
Name:
Date:
"Goal: Use the radioactive decay simulation to discover the patterns and mathematical laws that allow us to use rock crystals as geologic clocks."
Part 1: Predicting Trends
Sketch your prediction for how the percentage of Parent Element and Daughter Element will change over time in a rock crystal.
% of Element
Time (mya)
Sketch your prediction curves here.
Hypothesis:
How will the rate of decay change as time passes?
Part 2: Experimental Data
Using the simulation, conduct trials for different conditions. Record the time (mya) it takes to reach specific percentage thresholds.
Condition (Element & Width) Trial 1 (mya) Trial 2 (mya) Average Time (50%) Average Time (25%) K-40 (20 units) K-40 (40 units) U-238 (20 units) U-238 (40 units) U-235 (20 units)
Part 3: Decoding the Patterns
1. The Crystal Size Test
Compare your results for 20 units vs 40 units width. Did crystal size affect the rate of decay?
2. The "Half-Life" Constant
Look at your 50% average and your 25% average for any single element. What is the mathematical relationship between these two numbers?
Half-Life Values Found:
K-40
mya
U-238
mya
U-235
mya
Atomic Clock Slides Atomic Clocks
Reconstructing the Geologic History of Afar through Radioactive Decay
The Big Question
"Is the rock at Afar radioactive, and what can that tell us about the region's history?"
Past
When did these volcanoes erupt? How has the land changed over millions of years?
Future
Can we predict the next major geologic shift based on previous rates of change?
Geologic Clocks
All rocks containing radioactive elements undergo decay at a known, constant rate.
By measuring the amount of radioactive material left, we can determine the rock's absolute age.
Field Investigation: Afar
Scientists collected samples from across the Afar region. Each site (A-G) contains different rock formations.
Key Observation
Each sample contains either Potassium-40 (K-40) or Uranium-238 (U-238), but never both. Why?
Refer to the
The Transformation
Magma
Elements are mixed in liquid rock.
Crystals
Specific elements are locked in as rock cools.
Decay
Parent elements turn into daughter elements.
Spectrometers count these atoms
Simulating Decay
Embedded media
Open the Simulation
Record in Lab Journal
What's the Pattern?
Group Discussion:
Does crystal size affect the rate of decay?
Does the type of element (K-40 vs U-238) change the half-life?
The Half-Life Rule
"The time to reach 50% is identical to the time to get from 50% to 25%."
The Atomic Equation
Original Decay Model
\[ P_r = \left( \frac{1}{2} \right)^{(t/h)} \]
Solved for Time (\(t\))
\[ t = h \cdot \left( \frac{\ln(P_r)}{\ln(1/2)} \right) \]
\(P_r\)
Remaining Parent Ratio
\(t\)
Age of Rock (mya)
\(h\)
Element Half-Life
Time Detectives
Use spectrometer data to calculate the absolute age of samples A–G.
Mission Briefing
Use Calculator/Spreadsheet
Watch Significant Figures
Map Age vs. Location
Embedded media
The Geologic Story
"Some rocks in Afar are hundreds of millions of years old, while others formed only yesterday."
Final Analysis
How does the arrangement of ages (oldest on edges, youngest in center) prove our model of plate tectonics?
Afar Rock Chronology Worksheet Afar Rock Chronology
Analysis Report: Radiometric Dating of Volcanic Samples
Agent/Student:
Date of Analysis:
Calculation Reference
Standard Model
\[ P_r = \left( \frac{1}{2} \right)^{(t/h)} \]
Solved for Time (\(t\))
\[ t = h \cdot \frac{\ln(P_r)}{\ln(1/2)} \]
Data Precision
Use the first 5 significant figures for \(P_r\).
Constants (\(h\))
K-40: 1,250 mya
U-238: 4,500 mya
Variable Legend
\(P_r\) Parent Element remaining now
\(t\) Absolute age (Millions of Years)
\(h\) Constant Half-Life value
Series 1: Potassium-40 (K-40) Samples
Site ID Ratio (K-40 : Daughter) Remaining Parent (\(P_r\)) Calculated Age (\(t\)) A1 6249 : 1 0.99984 B2 1885.8 : 1 0.99947 C1 624.00 : 1 0.99840 D1 399.00 : 1 0.99750 E1 73.404 : 1 0.98656 F1 61.267 : 1 0.98394 Other:
Series 2: Uranium-238 (U-238) Samples
Site ID Ratio (U-238 : Daughter) Remaining Parent (\(P_r\)) Calculated Age (\(t\)) B1 1611.9 : 1 0.99938 D3 868.57 : 1 0.99885 G1 10.55 : 1 0.9134 G4 9.903 : 1 0.9083
Spatial Age Analysis
Mapping the history of the Afar region across site locations.
Region Approx. Age Range (mya) Region A Region B
Geologic Brief Teacher Guide Geologic Brief
Teacher Facilitation & Answer Key • Lesson 8
Geologic Survey P.2.8
"Time is written in the crystals."
Sample Site Distribution
Scientific Context
The Afar region is a unique triple-junction rift. Our samples are redrawn approximations of maps from Stab M, et al. (2015). Sites A-F are based on published locations, while G1-G4 were added for pedagogical comparison of continental vs. rift-center ages.
Key Geologic Patterns
The Sandwich Effect: Students should notice that the oldest rocks (G) are found on the western and eastern edges, while the youngest rocks (A) are found in the active center of the rift.
Lab Journal Key
Discovery 1: Crystal Size
Crystal size has zero effect on radioactive decay. The probability of an atom decaying is independent of the mass or container size. If students' data shows a difference, it is due to sampling error/fluctuation.
Discovery 2: Half-Life Constant
The time to reach 25% should be exactly double the time to reach 50%. This demonstrates the constant probability of decay over time (exponential decay).
K-40 Half-Life
~1,250 mya
U-238 Half-Life
~4,500 mya
U-235 Half-Life
~700 mya
Chronology Calculations
Decay Model
\[ P_r = (0.5)^{(t/h)} \]
Time Solution
\[ t = h \cdot \frac{\ln(P_r)}{\ln(0.5)} \]
Region Sample Sites Expected Age Range (mya) Region A A1 - A4 0.12 – 0.33 mya Region B B1 - B5 0.49 – 4.0 mya Region C C1 - C5 1.9 – 3.2 mya Region D D1 - D4 4.5 – 8.2 mya Region E E1 - E3 23 – 25 mya Region F F1 - F3 29 – 31 mya Region G G1 - G4 583 – 659 mya
Facilitation Tip: Significant Figures
Remind students that Significant Figures matter. All K-40 ratios now include 5 significant figures. Ask students to pay close attention to the first 5 numbers in their spreadsheet calculations to avoid drift in the final ages.
