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CALCULATING HALF-LIFE Aim: How can we measure how much of a radioactive element decayed? DO NOW: If we start with 4.5 grams of Radon- 222 and over a period.

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Presentation on theme: "CALCULATING HALF-LIFE Aim: How can we measure how much of a radioactive element decayed? DO NOW: If we start with 4.5 grams of Radon- 222 and over a period."— Presentation transcript:

1 CALCULATING HALF-LIFE Aim: How can we measure how much of a radioactive element decayed? DO NOW: If we start with 4.5 grams of Radon- 222 and over a period of time we have 3.4 grams left over. What is the fraction remaining of this sample? 3.4g / 4.5g =

2 What is half-life? The amount of time it takes for the mass of a radioactive sample to decay by half. Half-life is AMOUNT OF TIME Table N

3 EXAMPLE!! Consider a 10 g sample of Au-198. (Table N)  What decay mode does Au-198 have? (3) Alpha decay!  What half-life does Au-198 have? (4) 2.69 days

4 Let’s see Au-198 At 0 half-life or 0 days, there are 10 g present. After 1 half-life or 2.69 days, there are 5 g remaining. After 2 half-life or 5.38 (2 x 2.69) days, (5) 2.5grams remain. After 3 half-life or 8.07 (3 x 2.69) days, (6) 1.25 grams remain.

5 Calculating Fraction Remaining… What is a fraction? THE RATIO BETWEEN A PART AND A WHOLE. …NOW I NEED 8 VOLUNTEERS

6 Fraction Remaining # of Half-LivesFraction Remaining 01 1½ 2¼ 31/8 41/16 51/32

7 Example 1 If 1.00 gram of a 16.00 gram sample of sodium-25 remains unchanged after 237 seconds, what is the fraction remaining? Step 1: What was the mass of the original sample?  16.00 gram Step 2: What is the mass that is remaining after the given period of time?  1.00 grams Step 3: What is the fraction remaining?  1/16

8 EXAMPLE 3 If 1.00 gram of a 16.00 gram sample of sodium-25 remains unchanged after 237 seconds, how many half-lives have passed? Step 1: What was the mass of the original sample?  16.00 grams Step 2: What is the mass that is remaining after the given period of time?  1.00 grams Step 3: What is the fraction remaining?  1/16 Step 4: How many half-lives have passed?  4

9 Calculating total time FORMULA: # of half-lives x length of half-life = total time

10 Example 6 A sample of wood is found to contain 1/8 as much C-14 as ipresent in the wood of a living tree. How old is the tree? Step 1: Figure out the fraction remaining.  1/8 Step 2: Figure out the number of half- lives passed.  3 Step 3: Figure out the length of one half-life (Table N or given in the problem).  Step 4: Multiply the number of half-lives by the length of one half-life. 3 x =

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