Half- Life

Some minerals contain radioactive elements. 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. 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 Some examples Uranium, Radium, Plutonium Uranium, Radium, Plutonium

Transmutation Transmutation- a radioactive element changing (decaying) into a another substance Transmutation- a radioactive element changing (decaying) into a another substance dependent on HALF-LIFE dependent on HALF-LIFE HALF-LIFE  the time it takes for half of a radioactive sample to decay (turn into something else) 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 times can vary, depending upon the radioactive element, from a few fractions of a second to several million years

Half-Life Original Amount After One Half-Life After two half-lives Fraction = 1/1 Fraction = 1/2Fraction = 1/4 What fraction of the original population would be left after 3 half-lives? After 4?After 5? 1/81/161/32

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

Solving Half-Life Problems Every half-life problem will ask one of the following: Every half-life problem will ask one of the following: Time Time Fraction Fraction Sample Size Sample Size Number of half-lives Number of half-lives

1/164 1/83 1/42 1/21 1/10SampleTimeFraction # of Half- Lives Always the Same Changes Based upon Problem Table for Solving Half-Life Problems

For each problem Determine what is being asked (what is the question asking) 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) 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 Fill in the chart using the information from the problem Use your completed chart to solve 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 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 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 1- fill in the top row of your sample #1 chart in your notes

Sample Problem #1 # of Half Lives Fraction (Undecayed) TimeSample

Let’s try some… Sample Problem#1 A sample takes 0.05 seconds to decay 1 half-life 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 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 2- fill in the first two columns of your chart in your notes

Sample Problem #1 # of Half Lives Fraction (Undecayed) TimeSample 01/1 11/2 21/4 31/8 41/16 51/32

Let’s try some… Sample Problem#1 A sample takes 0.05 seconds to decay 1 half-life 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 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 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 STEP 3- fill in the “Time” column in your chart using the information from the problem

Sample Problem #1 # of Half Lives Fraction (Undecayed) TimeSample 01/10 sec 11/20.05 sec 21/40.10 sec 31/80.15 sec 41/ sec 51/ sec

Let’s try some… Sample Problem#1 A sample takes 0.05 seconds to decay 1 half-life 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: Determine your solution from the chart: 5 half- lives 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)? b. What fraction of the original sample will be left after this time (0.25 seconds)? Determine your solution from the chart: Determine your solution from the chart:

Sample Problem #1 # of Half Lives Fraction (Undecayed) TimeSample 01/10 sec 11/20.05 sec 21/40.10 sec 31/80.15 sec 41/ sec 51/ sec

Let’s try some… Sample Problem#1 b. What fraction of the original sample will be left after this time (0.25 seconds)? b. What fraction of the original sample will be left after this time (0.25 seconds)? Determine your solution from the chart: Determine your solution from the chart: 1/32 of the original sample 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? 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 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 Divide each number by 2 to fill in the next row

Sample Problem #1 # of Half Lives Fraction (Undecayed) TimeSample 01/10 sec 10 grams 11/20.05 sec 5 grams 21/40.10 sec 2.5 grams 31/80.15 sec 1.25 grams 41/ sec grams 51/ sec 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? c. If the original sample is 10 grams, how many grams are left after 0.25 seconds? Determine your solution using the chart: Determine your solution using the chart: grams grams

Sample Problem #2 If it takes a sample 12 hours to go through 4 half-lives, how long is each half-life? 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 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 FractionTimeSample 01/1 11/2 21/4 31/8 41/16 51/32