Radioactive Isotopes and Half Life 1

I can explain what a Radioactive Half-Life is and do a calculation with both a T-table and by equation. 2

Since radioactive elements are unstable, they decay, and change into different elements over time through Alpha, Beta and Gamma decay processes. Though not all elements are radioactive, many have one or more isotopes (nuclides) that are. Radioactive Isotopes 3

Radioactive Decay and Half Life The time required for an unstable element to decay to a stable form is measured in terms of HALF-LIVES. 1.The HALF-LIFE (T 1/2 ) of an element is the TIME it takes for one-half of a radioactive sample to decay to a stable form. 2.Each ISOTOPE (nuclide) has a unique T 1/2, ranging from fractions of a second to billions of years. 4

3.Each radioactive element decays into a new element that is stable over time. For example C-14 eventually decays into N The T1/2 of each element is constant. It’s like a clock keeping perfect time. For example, C-14 has a T1/2 of 5,730 years. Radioactive Decay and Half Life 5

6 In this practice problem, we will let a block of 16 squares represent atoms of the radioactive element Carbon-14 (C-14).

The shaded grid on the LEFT represents a sample of radioactive C-14 atoms decaying to stable N-14 atoms. NOTE: at the begin notice that no time has gone by and that 100% of the material is C-14. ***MOVE TO THE NEXT GRID BEFORE RECORDING ANY INFORMATION*** Half lives % C-14%N-14 Ratio of C 14 to N 14 Time Elapsed, in Years 7

Half lives % C 14 %N 14 Ratio of C 14 to N 14 Time Elapsed, in Years 0100%0%no ratio 0 8 At Time=0, no time has passed and no atoms have decayed yet! Now move to the next grid.

9 Now make an X through one half of the boxes, to indicate the passage of one half-life.

Half lives % C 14 %N 14 Ratio of C 14 to N 14 Time Elapsed, in Years 0100%0%no ratio0 150% 1:15730 XX XX XX XX 10

11 Now make an X through one half of the REMAINING boxes, to indicate the passage of another half-life.

Half lives % C 14 %N 14 Ratio of C 14 to N 14 Time Elapsed, in Years 0100%0%no ratio % 1: %75%1: XX XX XXXX XXXX 12

13 Now make an X through one half of the REMAINING boxes, to indicate the passage of another half-life.

Half lives % C-14%N-14 Ratio of C 14 to N 14 Time Elapsed, in Years 0100%0%no ratio0 150% 1: %75%1: %87.5%1: XX XXXX XXXX XXXX 14

15 Now make an X through one half of the REMAINING boxes, to indicate the passage of another half-life.

Half lives % C-14%N-14 Ratio of C 14 to N 14 Time Elapsed, in Years 0100%0%no ratio0 150% 1: %75%1: %87.5%1: %93.7%1: XXX XXXX XXXX XXXX 16

17 Now make an X through the REMAINING box, to indicate the passage of the final half- life.

Half lives % C-14%N-14 Ratio of C 14 to N 14 Time Elapsed, in Years 0100%0%no ratio0 150% 1: %75%1: %87.5%1: %93.7%1: %100%no ratio28650 XXXX XXXX XXXX XXXX 18

years were required for this sample of radioactive C-14 atoms to decay to stable N-14 atoms! While the T1/2 of C-14 seems long at 5730 years, many radioisotopes have half-life values in the millions or billions of years.

20 Half-Life Values of some Common Isotopes ElementIsotopeHalf-Life Hydrogen H years Carbon C years Sodium Na years PhosphorusP days Sulfur S days ChlorineCl ,000 years Potassium K-40 1,277,000,000 years Iron Fe years Cobalt Co days Uranium U-238 4,468,000,000 years Plutonium Pu years Technitium Tc hours (medical use for CT/MRI and other scans) Iodine I days (medical use to treat thyroid cancer)

21 Practice Problems – Use a T-table to make these half-life calculations. 1)How long will it take 275 grams of Phosphorus-32 to decay? Consider stable when less than 1 gram of the atoms are radioactive. 2)A 1000 g sample of Iodine-131 is delivered to a hospital to treat thyroid cancer patients. How many days will this supply be usable?

22 To work the problem: 1.Draw the T-table as shown on the next slide. 2.Fill in the info at the top for P-32 and T1/2 = days. 3.Label the left side of the table as “time” in days here and the “amount remaining” in grams. 4.Start out with time 0 and 275 grams. 5.Next, one half-life has elapsed, so mark the time as days, and the amount remaining is ½ the original amount, or ½ of 275 g which is grams. 6.Move back to the time side, ADD another half-life (be careful to add one half life not multiply!) and take half of the previous mass. 7.Repeat Step 6 until the amount remaining drops BELOW 1 gram!

23 Time, Amount in Remaining, in grams T-table for _________, T 1/2 = ______

24 0 days 275 g P days

25 0 days 275 g days g P days

26 0 days 275 grams days grams days grams P days YOU complete the rest of the table until the mass remaining is less than 1 gram. ADD a T 1/2 each time Take ½ the amount remaining each time.

27 Work the second problem on your OWN!