CALCULATING HALF-LIFE Aim: How can we measure how much of a radioactive element decayed?

1. CALCULATING HALF-LIFEAim: 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! Whathalf-life does Au-198 have? (4) 2.69 days

4. Let’s see Au-198

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

6. Fraction Remaining

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 ipresentin 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 =