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Question of the DayQuestion of the DayQuestion of the DayQuestion of the Day
Question: How are the two kinds of dating (aging) similar? Different?
Answer: … … …
Turn In:-What’s Up
-Computer Lab: Rocks & Minerals-Current Event Article, Summary, & Evaluation
(staple together)
Some minerals contain radioactive Some minerals contain radioactive elements. elements.
The rate at which these elements The rate at which these elements decay (turn into other elements) can decay (turn into other elements) can help us determine the absolute age help us determine the absolute age of the rock that contains that mineral.of the rock that contains that mineral.
Some examplesSome examples Uranium, Radium, PlutoniumUranium, Radium, Plutonium
TransmutationTransmutation
Transmutation- a radioactive Transmutation- a radioactive element changing (decaying) element changing (decaying) into a another substanceinto a another substance
dependent on HALF-LIFEdependent on HALF-LIFEHALF-LIFEHALF-LIFE the time it takes the time it takes
for half of a radioactive sample for half of a radioactive sample to decay (turn into something to decay (turn into something else)else)
Half-LifeHalf-Life
Half-Life times can vary, Half-Life times can vary, depending upon the depending upon the radioactive element, from a radioactive element, from a few fractions of a second to few fractions of a second to several million yearsseveral million years
Half-LifeHalf-Life
Original Amount After One Half-Life After two half-lives
Fraction = 1/1 Fraction = 1/2 Fraction = 1/4
What fraction of the original population would be left after 3 half-lives? After 4? After 5?
1/8 1/16 1/32
Why is this important?Why is this important?
How long it takes for certain How long it takes for certain elements to decayelements to decay
Can help us with absolute datingCan help us with absolute dating Helps scientists estimate the ages Helps scientists estimate the ages
of rocks and fossilsof rocks and fossils
Solving Half-Life ProblemsSolving Half-Life Problems
Every half-life problem will ask one Every half-life problem will ask one of the following:of the following: TimeTime FractionFraction Sample SizeSample Size Number of half-livesNumber of half-lives
1/161/1644
1/81/833
1/41/422
1/21/211
1/11/100
SampleSampleTimeTimeFractionFraction# of Half-# of Half-LivesLives
Always the Same Changes Based upon Problem
Table for Solving Half-Life Problems
For each problemFor each problem
Determine what is being asked (what Determine what is being asked (what is the question asking)is the question asking)
Draw a picture of the amount of Draw a picture of the amount of original sample left after radioactive original sample left after radioactive decay (if necessary)decay (if necessary)
Fill in the chart using the information Fill in the chart using the information from the problemfrom the problem
Use your completed chart to solve Use your completed chart to solve the problemthe problem
LetLet’’s try some…s try some…Sample Problem#1Sample Problem#1
A sample takes 0.05 seconds to A sample takes 0.05 seconds to decay 1 half-lifedecay 1 half-lifea. How many half-lives will have a. How many half-lives will have passed after 0.25 seconds?passed after 0.25 seconds?b. What fraction of the original b. What fraction of the original sample will be left after this time sample will be left after this time (0.25 seconds)?(0.25 seconds)?c. If the original sample is 10 grams, c. If the original sample is 10 grams, how many grams are left after 0.25 how many grams are left after 0.25 seconds?seconds?
LetLet’’s try some…s try some…Sample Problem#1Sample Problem#1
A sample takes 0.05 seconds to A sample takes 0.05 seconds to decay 1 half-lifedecay 1 half-lifea. How many half-lives will have a. How many half-lives will have passed after 0.25 seconds?passed after 0.25 seconds? STEP 1- fill in the top row of your STEP 1- fill in the top row of your
sample #1 chart in your notessample #1 chart in your notes
LetLet’’s try some…s try some…Sample Problem#1Sample Problem#1
A sample takes 0.05 seconds to A sample takes 0.05 seconds to decay 1 half-lifedecay 1 half-lifea. How many half-lives will have a. How many half-lives will have passed after 0.25 seconds?passed after 0.25 seconds? STEP 1- fill in the top row of your STEP 1- fill in the top row of your
sample #1 chart in your notessample #1 chart in your notes STEP 2- fill in the first two columns STEP 2- fill in the first two columns
of your chart in your notesof your chart in your notes
Sample Problem #1
# of Half Lives
Fraction (Undecayed)
Time Sample
0 1/1
1 1/2
2 1/4
3 1/8
4 1/16
5 1/32
LetLet’’s try some…s try some…Sample Problem#1Sample Problem#1
A sample takes 0.05 seconds to decay A sample takes 0.05 seconds to decay 1 half-life1 half-lifea. How many half-lives will have a. How many half-lives will have passed after 0.25 seconds?passed after 0.25 seconds? STEP 1- fill in the top row of your sample STEP 1- fill in the top row of your sample
#1 chart in your notes#1 chart in your notes STEP 2- fill in the first two columns of STEP 2- fill in the first two columns of
your chart in your notesyour chart in your notes STEP 3- fill in the STEP 3- fill in the ““TimeTime”” column in column in
your chart using the information your chart using the information from the problemfrom the problem
Sample Problem #1
# of Half Lives
Fraction (Undecayed)
Time Sample
0 1/1 0 sec
1 1/2 0.05 sec
2 1/4 0.10 sec
3 1/8 0.15 sec
4 1/16 0.20 sec
5 1/32 0.25 sec
LetLet’’s try some…s try some…Sample Problem#1Sample Problem#1
A sample takes 0.05 seconds to A sample takes 0.05 seconds to decay 1 half-lifedecay 1 half-lifea. How many half-lives will have a. How many half-lives will have passed after 0.25 seconds?passed after 0.25 seconds?
Determine your solution from the Determine your solution from the chart:chart: 5 half- lives 5 half- lives
LetLet’’s try some…s try some…Sample Problem#1Sample Problem#1
b. What fraction of the original b. What fraction of the original sample will be left after this time sample will be left after this time (0.25 seconds)?(0.25 seconds)?
Determine your solution from the Determine your solution from the chart:chart:
Sample Problem #1
# of Half Lives
Fraction (Undecayed)
Time Sample
0 1/1 0 sec
1 1/2 0.05 sec
2 1/4 0.10 sec
3 1/8 0.15 sec
4 1/16 0.20 sec
5 1/32 0.25 sec
LetLet’’s try some…s try some…Sample Problem#1Sample Problem#1
b. What fraction of the original b. What fraction of the original sample will be left after this time sample will be left after this time (0.25 seconds)?(0.25 seconds)?
Determine your solution from the Determine your solution from the chart:chart: 1/32 of the original sample1/32 of the original sample
LetLet’’s try some…s try some…Sample Problem#1Sample Problem#1
c. If the original sample is 10 c. If the original sample is 10 grams, how many grams are left grams, how many grams are left after 0.25 seconds?after 0.25 seconds? Complete the final column of your Complete the final column of your
chart starting with 10 grams at 0 half-chart starting with 10 grams at 0 half-liveslives
Divide each number by 2 to fill in the Divide each number by 2 to fill in the next rownext row
Sample Problem #1
# of Half Lives
Fraction (Undecayed)
Time Sample
0 1/1 0 sec 10 grams
1 1/2 0.05 sec 5 grams
2 1/4 0.10 sec 2.5 grams
3 1/8 0.15 sec 1.25 grams
4 1/16 0.20 sec 0.625 grams
5 1/32 0.25 sec 0.3125 grams
LetLet’’s try some…s try some…Sample Problem#1Sample Problem#1
c. If the original sample is 10 c. If the original sample is 10 grams, how many grams are left grams, how many grams are left after 0.25 seconds?after 0.25 seconds?
Determine your solution using the Determine your solution using the chart:chart: 0.3125 grams0.3125 grams
Sample Problem #2Sample Problem #2
If it takes a sample 12 hours to go If it takes a sample 12 hours to go through 4 half-lives, how long is through 4 half-lives, how long is each half-life?each half-life? Divide the amount of time by the Divide the amount of time by the
number of half-lives that have passednumber of half-lives that have passed
12 hours ÷12 hours ÷
4 hours =4 hours =
3 hours3 hours