𝐴= 𝐴 𝑜 𝑒 −𝜆𝑡 LAB #2 Radioactive decay calculation ; 𝐴= 𝐴 𝑜 𝑒 −𝜆𝑡 𝜆= 𝑙𝑛2 𝑇 1/2 𝐴= 𝐴 𝑜 𝑒 −0.693 𝑇 1/2 𝑡 Where as: A= activity at time (t) 𝐴 𝑜 = the initial activity (t=0) 𝜆= decay constant t= time 𝑇 1/2 = the half-life 1 𝐶𝑖= 10 12 𝑝𝐶𝑖 1 𝐶𝑖= 10 3 𝑚𝐶𝑖 1 𝐶𝑖= 10 −6 𝑀𝐶𝑖 1 𝐶𝑖= 3.7×10 10 𝐵𝑞 dpm 𝐶𝑖=𝑐𝑢𝑟𝑖 𝑝𝐶𝑖=𝑝𝑖𝑐𝑜𝑐𝑢𝑟𝑖𝑒 𝑚𝐶𝑖=𝑚𝑖𝑙𝑙𝑖𝑐𝑢𝑟𝑖𝑒 𝑀𝐶𝑖=𝑚𝑒𝑔𝑎𝑐𝑢𝑟𝑖𝑒 𝐵𝑞=𝑏𝑒𝑐𝑞𝑢𝑒𝑟𝑒𝑙 Very Important Note:- A & 𝐴 𝑜 should have the same unit Also, t & 𝑇 1/2 should have the same unit For instant, if (A) is in mCi ( 𝐴 𝑜 ) MUST be in mCi And if (t) is in years ( 𝑇 1/2 ) MUST be in years

Example1 :- Given 10 mCi of 32P, which has a half-life of 14.2 days, find the quantity remaining after 60days. 𝐴= 𝐴 𝑜 𝑒 −0.693 𝑇 1/2 𝑡 𝐴 0 =10𝑚𝐶𝑖, 𝐴 𝑡 =??? 𝑇 1/2 =14.2𝑑𝑎𝑦𝑠 𝑡=60𝑑𝑎𝑦𝑠 𝐴 𝑡 =10 𝑒 −𝑙𝑛2 14.4 60 𝐴 𝑡 =10 𝑒 −2.93 𝐴 𝑡 =10×0.0534 ∴𝐴 𝑡 =0.534 𝑚𝐶𝑖 Example2 :- if the initial activity of the radionuclide mentioned above was 52 µCi, then the activity after 4 hours would be: 𝐴 0 =52µ𝐶𝑖, 𝐴 𝑡 =??? 𝑇 1/2 =14.2𝑑𝑎𝑦𝑠 𝑡=4ℎ𝑜𝑢𝑟𝑠=0.166 𝑑𝑎𝑦𝑠 𝐴 𝑡 =52 𝑒 −𝑙𝑛2 14.4 0.16 𝐴 𝑡 =52 𝑒 −7.70× 10 −3 𝐴 𝑡 =52×0.992 𝐴 𝑡 =51.6 µ𝐶𝑖

B) To how many MBq does this correspond? (99mTc Half life =6 hr) Ex.3; A) If 20mCi of 99mTc is needed for a diagnostic test, and if 4 hours elapse between preparing of the radioisotope and its use in the test, how many mCi must be prepared? B) To how many MBq does this correspond? (99mTc Half life =6 hr) 𝐴= 𝐴 𝑜 𝑒 −0.693 𝑇 1/2 𝑡 𝐴 0 =20𝑚𝐶𝑖, 𝐴 𝑡 =??? 𝑇 1/2 =6ℎ𝑟 𝑡=−4 ℎ𝑟 A) 𝐴 𝑡 =20 𝑒 −𝑙𝑛2 6 −4 𝐴 𝑡 =20 𝑒 0.46 𝐴 𝑡 =20×1.59 ∴𝐴 𝑡 =31.8 𝑚𝐶𝑖 B) ∴𝐴 𝑡 =31.8 𝑚𝐶𝑖=0.0318𝐶𝑖=1176600000𝐵𝑞=1176.6 𝑀𝐵𝑞

B) and 4 p.m. on the same day (t1/2 =6 hr) 𝐴= 𝐴 𝑜 𝑒 −0.693 𝑇 1/2 𝑡 Ex.4; At 11 a.m. the99mTc radioactivity was measured as 9 mCi on a certain day. What was the activity at 8 a.m. B) and 4 p.m. on the same day (t1/2 =6 hr) 𝐴= 𝐴 𝑜 𝑒 −0.693 𝑇 1/2 𝑡 𝐴 0 =9𝑚𝐶𝑖, 𝐴 𝑡 =??? 𝑇 1/2 =6ℎ𝑟 𝐴) 𝑡 1 =11𝑎𝑚 𝑡𝑜 8𝑎𝑚=−3 ℎ𝑟 B) 𝑡 2 =11𝑎𝑚 𝑡𝑜 4𝑝𝑚=5 ℎ𝑟 A) 𝐴 𝑡 =9 𝑒 −𝑙𝑛2 6 −3 𝐴 𝑡 =9 𝑒 0.35 𝐴 𝑡 =9×1.41 ∴𝐴 𝑡 =12.7 𝑚𝐶𝑖 B) 𝐴 𝑡 =9 𝑒 −𝑙𝑛2 6 5 𝐴 𝑡 =9 𝑒 −0.58 𝐴 𝑡 =9×0.56 ∴𝐴 𝑡 =5.05 𝑚𝐶𝑖

Ex.5; What is the half-life of an isotope if it decays to 12.5% of its radioactivity in 18 minutes? 𝐴= 𝐴 𝑜 𝑒 −0.693 𝑇 1/2 𝑡 𝐴 0 =100%, 𝐴 𝑡 =12.5% 𝑇 1/2 =??? 𝑡=18min 𝐴 𝐴 𝑜 = 𝑒 −0.693 𝑇 1/2 𝑡 𝐴 𝑡 𝐴 𝑜 = 12.5 100 = 𝑒 −𝑙𝑛2 𝑇 1/2 18 12.5 100 = 𝑒 −𝑙𝑛2 𝑇 1/2 18 𝑙𝑛 12.5 100 =𝑙𝑛 𝑒 −𝑙𝑛2 𝑇 1/2 18 𝑙𝑛 12.5 100 = −𝑙𝑛2 𝑇 1/2 18 ∴ 𝑇 1/2 = −𝑙𝑛2 𝑙𝑛 12.5/100 18=6 𝑚𝑖𝑛

Practice Problems 𝐴= 𝐴 𝑜 𝑒 −0.693 𝑇 1/2 𝑡 𝐴= 𝐴 𝑜 𝑒 −0.693 𝑇 1/2 𝑡 1. A Phosphorous-32 source has a half-life of 14.28 days and had an activity of 75,000 dpm as of 12/2/92. What was the activity as of 12/28/92? 𝐴 0 =75,000 𝑑𝑝𝑚, 𝐴 𝑡 =??? 𝑇 1/2 =14.28𝑑𝑎𝑦 𝑡=12/2/92 𝑡𝑜 12/28/92=26𝑑𝑎𝑦 2. A 55mCi Sr-90 source was assayed on 6/1/88. What would the activity be on 6/1/93? (The half-life of Sr-90 is 29.1 years) H.W. 𝐴 0 =55𝑚𝐶𝑖, 𝐴 𝑡 =??? 𝑇 1/2 =29.1𝑦𝑒𝑎𝑟𝑠 𝑡=6/1/88 𝑡𝑜 6/1/93=5𝑦𝑒𝑎𝑟𝑠 3. An 60 mCi iodine solution of I-131 was created and then left on a laboratory shelf for two weeks before it was used. What was the activity of the solution at the time it was used? (Iodine-131 has a half-life of 8.04 days) 𝐴 0 =???, 𝐴 𝑡 =60𝑚𝐶𝑖, 𝑇 1/2 =8.04𝑑𝑎𝑦𝑠 𝑡=− 4×7 =−28𝑑𝑎𝑦𝑠 4. A radon air sample was collected and then counted 4 hours later. If the sample count showed an activity of 5E4 pCi, what was the activity on the sample at the time it was collected? (Radon-222 has a half-life of 3.8235 days) 𝐴 0 =???, 𝐴 𝑡 =5𝐸4 𝑝𝐶𝑖 𝑇 1/2 =3.8235 𝑑𝑎𝑦𝑠 𝑡=− 4 24 =0.166 𝑑𝑎𝑦𝑠

Practice Problems 𝐴= 𝐴 𝑜 𝑒 −0.693 𝑇 1/2 𝑡 𝐴= 𝐴 𝑜 𝑒 −0.693 𝑇 1/2 𝑡 5. A 10.5 Ci Co-60 radiography source was prepared 3 years ago, having a half-life of 5.271 years. What is the activity today? 𝐴 0 =10.5 𝐶𝑖, 𝐴 𝑡 =??? 𝑇 1/2 =5.271 𝑦𝑒𝑎𝑟𝑠 𝑡=3 𝑦𝑒𝑎𝑟𝑠 −𝑡𝑜𝑑𝑎𝑦= 𝑦𝑒𝑎𝑟𝑠 6. A pure alpha source reads 244,000 dpm today. It is a Po-210 source which has a half-life of 138.38 days. If the source was manufactured a year ago, what the activity at the time it was manufactured? 𝐴 0 =244000 𝑑𝑝𝑚, 𝐴 𝑡 =??? 𝑇 1/2 =138.8 𝑑𝑎𝑦𝑠 𝑡=𝑡𝑜𝑑𝑎𝑦−1𝑦𝑒𝑎𝑟 𝑎𝑔𝑜= 𝑑𝑎𝑦𝑠 7. A Cs-137 source has an activity of 750 mCi, with a half-life of 30.17 years. How long will it take for the source to be read less than 100 mCi? H.W. 𝐴 0 =750𝑚𝐶𝑖, 𝐴 𝑡 =100𝑚𝐶𝑖 𝑇 1/2 =30.17 𝑦𝑒𝑎𝑟𝑠 𝑡=??? 8. An air sample was collected in a thorium storage building and was counted immediately, yielding 2.5E3 pCi/l. The sample was recounted 5 minutes later giving an activity of only 59.4 pCi/l. What is the half-life and the most likely isotope on the sample? H.W. 𝐴 0 =2.5𝐸3𝑝𝐶𝑖/𝑙, 𝐴 𝑡 =59.4𝑝𝐶𝑖/𝑙 𝑇 1 2 =??? 𝑡=5𝑚𝑖𝑛𝑠

A curie (Ci) is a deprecated non-SI unit of radioactivity defined as 1 Ci = 3.7 × 10¹⁰ decays per second. Therefore, 1 Ci = 3.7·10¹⁰ Bq (exactly) and 1 Bq = 2.7027·10⁻¹¹ Ci. One curie is roughly the activity of 1 gram of the radium isotope ²²⁶Ra. A becquerel (Bq) is the SI derived unit of radiation activity. The Bq is defined as the activity of a quantity of radioactive material in which one nucleus decays per second. The becquerel is therefore equivalent to an inverse second, s⁻¹.