1. 𝐴= 𝐴 𝑜 𝑒 −𝜆𝑡 LAB #2 Radioactive decay calculation ;
𝐴= 𝐴 𝑜 𝑒 −𝜆𝑡
𝜆= 𝑙𝑛2 𝑇 1/2
𝐴= 𝐴 𝑜 𝑒 − 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= 𝑝𝐶𝑖
1 𝐶𝑖= 𝑚𝐶𝑖
1 𝐶𝑖= 10 −6 𝑀𝐶𝑖
1 𝐶𝑖= 3.7× 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

2. 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 − 𝑇 1/2 𝑡
𝐴 0 =10𝑚𝐶𝑖, 𝐴 𝑡 =??? 𝑇 1/2 =14.2𝑑𝑎𝑦𝑠 𝑡=60𝑑𝑎𝑦𝑠
𝐴 𝑡 =10 𝑒 −𝑙𝑛
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 −𝑙𝑛
𝐴 𝑡 =52 𝑒 −7.70× 10 −3
𝐴 𝑡 =52×0.992
𝐴 𝑡 =51.6 µ𝐶𝑖

3. 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 − 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= 𝐵𝑞= 𝑀𝐵𝑞

4. 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 − 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

5. 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 − 𝑇 1/2 𝑡
𝐴 0 =100%, 𝐴 𝑡 =12.5% 𝑇 1/2 =??? 𝑡=18min
𝐴 𝐴 𝑜 = 𝑒 − 𝑇 1/2 𝑡
𝐴 𝑡 𝐴 𝑜 = = 𝑒 −𝑙𝑛2 𝑇 1/2 18
= 𝑒 −𝑙𝑛2 𝑇 1/2 18
𝑙𝑛 =𝑙𝑛 𝑒 −𝑙𝑛2 𝑇 1/2 18
𝑙𝑛 = −𝑙𝑛2 𝑇 1/2 18
∴ 𝑇 1/2 = −𝑙𝑛2 𝑙𝑛 12.5/ =6 𝑚𝑖𝑛

6. Practice Problems 𝐴= 𝐴 𝑜 𝑒 −0.693 𝑇 1/2 𝑡
𝐴= 𝐴 𝑜 𝑒 − 𝑇 1/2 𝑡
1. A Phosphorous-32 source has a half-life of 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 days)
𝐴 0 =???, 𝐴 𝑡 =5𝐸4 𝑝𝐶𝑖 𝑇 1/2 = 𝑑𝑎𝑦𝑠 𝑡=− 4 24 =0.166 𝑑𝑎𝑦𝑠

7. Practice Problems 𝐴= 𝐴 𝑜 𝑒 −0.693 𝑇 1/2 𝑡
𝐴= 𝐴 𝑜 𝑒 − 𝑇 1/2 𝑡
5. A 10.5 Ci Co-60 radiography source was prepared 3 years ago, having a half-life of 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 days. If the source was manufactured a year ago, what the activity at the time it was manufactured?
𝐴 0 = 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 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 =??? 𝑡=5𝑚𝑖𝑛𝑠

8. 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 = ·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.