Half- Life

 Some minerals contain radioactive elements.  The rate at which these elements decay (turn into other elements) can help us determine the absolute age of the rock that contains that mineral.

 Some examples  Uranium, Radium, Plutonium

Transmutation

   Transmutation- a radioactive element changing (decaying) into a another substance dependent on HALF-LIFE HALF-LIFE  the time it takes for half of a radioactive sample to decay (turn into something else)

Half-Life

 Half-Life times can vary, depending upon the radioactive element, from a few fractions of a second to several million years

Half-Life

Original Amount

Fraction = 1/1

After One Half-Life

Fraction = 1/2

After two half-lives

Fraction = 1/4 What fraction of the original population would be left after 3 half-lives?

1/8 After 4? 1/16 After 5?

1/32

Why is this important?

 How long it takes for certain elements to decay  Can help us with absolute dating  Helps scientists estimate the ages of rocks and fossils

Solving Half-Life Problems

 Every half-life problem will ask one of the following:     Time Fraction Sample Size Number of half-lives

Table for Solving Half-Life Problems # of Half Lives Fraction Time Sample 0 1/1 1 2 3 4 1/2 1/4 1/8 1/16

Always the Same Changes Based upon Problem

For each problem

 Determine what is being asked (what is the question asking)  Draw a picture of the amount of original sample left after radioactive decay (if necessary)  Fill in the chart using the information from the problem  Use your completed chart to solve the problem

Let’s try some… Sample Problem#1

 A sample takes 0.05 seconds to decay 1 half-life a. How many half-lives will have passed after 0.25 seconds?

b. What fraction of the original sample will be left after this time (0.25 seconds)?

c. If the original sample is 10 grams, how many grams are left after 0.25 seconds?

Let’s try some… Sample Problem#1

 A sample takes 0.05 seconds to decay 1 half-life a. How many half-lives will have passed after 0.25 seconds?



STEP 1- fill in the top row of your sample #1 chart in your notes

# of Half Lives

0 1 2 3 4 5 Sample Problem #1

Fraction (Undecayed) Time Sample

Let’s try some… Sample Problem#1

 A sample takes 0.05 seconds to decay 1 half-life a. How many half-lives will have passed after 0.25 seconds?

  STEP 1- fill in the top row of your sample #1 chart in your notes

STEP 2- fill in the first two columns of your chart in your notes

# of Half Lives

0 1 2 3 4 5 Sample Problem #1

Fraction (Undecayed)

1/1

Time

1/2 1/4 1/8 1/16 1/32

Sample

Let’s try some… Sample Problem#1

 A sample takes 0.05 seconds to decay 1 half-life a. How many half-lives will have passed after 0.25 seconds?

   STEP 1- fill in the top row of your sample #1 chart in your notes STEP 2- fill in the first two columns of your chart in your notes

STEP 3- fill in the “Time” column in your chart using the information from the problem

# of Half Lives

0 1 2 3 4 5 Sample Problem #1

Fraction (Undecayed)

1/1

Time

0 sec 1/2 0.05 sec 1/4 1/8 1/16 1/32 0.10 sec 0.15 sec 0.20 sec 0.25 sec

Sample

Let’s try some… Sample Problem#1

 A sample takes 0.05 seconds to decay 1 half-life a. How many half-lives will have passed after 0.25 seconds?

 Determine your solution from the chart:  5 half- lives

Let’s try some… Sample Problem#1

 b. What fraction of the original sample will be left after this time (0.25 seconds)?

 Determine your solution from the chart:

# of Half Lives

0 1 2 3 4 5 Sample Problem #1

Fraction (Undecayed)

1/1

Time

0 sec 1/2 0.05 sec 1/4 1/8 1/16 1/32 0.10 sec 0.15 sec 0.20 sec 0.25 sec

Sample

Let’s try some… Sample Problem#1

 b. What fraction of the original sample will be left after this time (0.25 seconds)?

 Determine your solution from the chart:  1/32 of the original sample

Let’s try some… Sample Problem#1

 c. If the original sample is 10 grams, how many grams are left after 0.25 seconds?

  Complete the final column of your chart starting with 10 grams at 0 half-lives Divide each number by 2 to fill in the next row

# of Half Lives

0 1 2 3 4 5 Sample Problem #1

Fraction (Undecayed)

1/1

Time

0 sec 1/2 1/4 1/8 1/16 1/32 0.05 sec 0.10 sec 0.15 sec 0.20 sec 0.25 sec

Sample

10 grams 5 grams 2.5 grams 1.25 grams 0.625 grams 0.3125 grams

Let’s try some… Sample Problem#1

 c. If the original sample is 10 grams, how many grams are left after 0.25 seconds?

 Determine your solution using the chart:  0.3125 grams

Sample Problem #2

 If it takes a sample 12 hours to go through 4 half-lives, how long is each half-life?

 Divide the amount of time by the number of half-lives that have passed 12 hours ÷ 4 half lives = 3 hours per half life

# of Half Lives

0 1 2 3 4 5

Fraction

1/1 1/2 1/4 1/8 1/16 1/32

Time Sample