Half- LifeHalf- Life

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

Let’s try some…Let’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?

Let’s try some…Let’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

Sample Problem #1

# of Half Lives

Fraction (Undecayed)

Time Sample

0

1

2

3

4

5

Let’s try some…Let’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

Let’s try some…Let’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 “Time” column in STEP 3- fill in the “Time” 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

Let’s try some…Let’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

Let’s try some…Let’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

Let’s try some…Let’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

Let’s try some…Let’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

Let’s try some…Let’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 half lives =4 half lives =

3 hours per half life3 hours per half life

# of Half Lives

Fraction Time Sample

0 1/1

1 1/2

2 1/4

3 1/8

4 1/16

5 1/32