Radioactivity and nuclear transformation

1. Lecture 7: May, 12, 2014 Shahid Younas RADIOACTIVITY & NUCLEAR TRANSFORMATION

2. INTRODUCTION Lecture 7 Radioactivity burst into the world without warning.

3. INTRODUCTION Lecture 7 Antoine-Henri Becquerel Director of Paris Museum of Natural History

4. INTRODUCTION Lecture 7 Becquerel began testing samples from his father’s collection. He was particularly interested in luminescent Uranium mineral. It was used to color ceramics and glass.

5. INTRODUCTION Lecture 7 Do you know why Uranium was given this name? After the name of newly discovered planet Uranus in those days.

6. INTRODUCTION Lecture 7 He believed that a heavy mineral would be most suitable for converting visible light into x-rays. Hennery received astonishing intense image on a cloudy day. Phosphorescent & fluorescent material emits light only if they are exposed to light.

7. INTRODUCTION Lecture 7 Silvanus P. Thompson- a British Electrical Engineer. Uranium compound gave off invisible rays. Hyper-phosphorescence

8. INTRODUCTION Lecture 7 Becquerel believed that effect would fade if he waited long enough. Hours turned into days, weeks, months; yet even after more than a year; Uranium’s power could not be abated.

9. INTRODUCTION Lecture 7 Do you know what is the half life of Uranium? U-238 : 447 Billion Years U-235: 704 Million Years

10. INTRODUCTION Lecture 7 He tried to destroy Uranium’s power by dissolving and re-crystalizing to retain his philosophy of phosphorescence. But All in Vain.

11. INTRODUCTION Lecture 7 Innocent Henry discovered about his rays that these, Electrified air Pass through cardboard, aluminum, copper and platinum Penetrate Opaque materials- property of x-rays

12. INTRODUCTION Lecture 04 The ability to pass through opaque materials suggests that uranium rays were a type of x rays. He believed them as “Mysterious Rays”.

13. Radioactivity Lecture 7 Process of spontaneous decay and transformation of unstable atomic nuclei accompanied with the emission of nuclear particles and/or nuclear radiation .

14. Radioactivity Lecture 7 Henri worked on Uranium. Do you know on which source Madam Curie worked? Radium

15. Radionuclide Decay Terms and Relationships Lecture 7 Activity: Number of radioactive atoms (N) undergoing nuclear transformation per unit time (t). A = - dN / dt Minus sign shows that radioactive atoms decreases with time.

16. Radionuclide Decay Terms and Relationships Lecture 7 Activity Tradition unit is Curie ( Ci ) 1 µ Ci = 2.22 x 10 6 dpm S.I. unit is Becquerel ( Bq ) Becquerel is one disintegration per second ( dps )

17. Radionuclide Decay Terms and Relationships Lecture 7 Do you know the relation between Henry Becquerel and Curie? Henry was cousin of Curie. Curie and Henry studied same high school Henry and Curie shared first noble prize. 1 milli Curie = 37 MBq

18. Radionuclide Decay Terms and Relationships Lecture 7 Decay Constant λ : Number of radioactive atoms decaying per unit time ( dN / dt ) is proportional to the number of unstable atoms (N) Proportionality can be transformed into an equality by a constant

19. Radionuclide Decay Terms and Relationships Lecture 7 Decay Constant: Decay constant is equal to the fraction of the number of radioactive atoms remaining in a sample that decay per unit time. A = λ N Decay constant is characteristic of each radionuclide.

20. Radionuclide Decay Terms and Relationships Lecture 7 Decay constant for 99 Mo is 0.252 per day. Do you know the decay constant for technetium-99m? 0.115 per hour

21. Radionuclide Decay Terms and Relationships Lecture 7 Physical Half Life: Time required for number of radioactive atoms in a sample to decrease by one half. . N = N o / 2 n N is number of radioactive atoms remaining No is the initial number of radioactive atoms n is the number of half lives.

22. Radionuclide Decay Terms and Relationships Lecture 7 Physical Half Life: After ten half-lives number of radioactive atoms in a sample is reduced by ~ a thousand and after twenty these reduced to a million.

23. Radionuclide Decay Terms and Relationships Lecture 7 Physical Half Life: Decay constant and physical half life are related as; λ = ln 2 / T 1/2 λ = 0.693 / T 1/2

24. Radionuclide Decay Terms and Relationships Lecture 7 If we mix 99m Tc and 131 I with each other. How would you find the decay of the mixture? Mixture Rule or otherwise count for the longest half life

25. Radionuclide Decay Terms and Relationships Lecture 7 Physical Half Life & Decay Constant Radionuclide Symbol T 1/2 λ Fluorine 18 F 110 m 0.0063 / m Technetium 99m Tc 6.02 hrs 0.1151/ hr Iodine 131 I 8.02 d 0.0864 / d Thallium 201 Tl 3.04 d 0.2281/d Gallium 67 Ga 3.26 d 0.2126 / d Iodine 125 I 59.41 d 0.0117 / d

26. Radionuclide Decay Terms and Relationships Lecture 7 Fundamental Decay Equation: Decay constant and physical half life are related as; N t = N o e - λ t or A t = A o e - λ t

27. Radionuclide Decay Terms and Relationships Lecture 7 Physical Half Life: N t = number of radioactive atoms at time t A t = activity at time t N o = initial number of radioactive atoms A o = initial activity e = base of natural logarithm λ = decay constant t = time

28. Radionuclide Decay Terms and Relationships Lecture 7 NUMERICALS A nuclear medicine technologist injects a patient with 500 µCi of indium-111 labeled autologous platelets (T 1/2 = 2.81 days) forty hours later the patient is imaged. Assuming that none of the activity was excreted, how much activity remains at the time of imaging?

29. Radionuclide Decay Terms and Relationships Lecture 7 NUMERICAL-1 Step 1: Collection of Data A o = 500 uCi T 1/2 = 2.82 days t = 48 hrs A t = ? NUMERICAL-1 Step 2: Look at the Units time t and half life should be in same unit. Pick the relevant equation N = N o / 2 n λ = 0.693 / T 1/2 A t = A o e – λ t

30. Radionuclide Decay Terms and Relationships Lecture 7 NUMERICAL-1 Step 3: March towards Solution λ = 0.693 / T 1/2 λ = 0.693 / 2.82 = 0.246 / day A t = A o e – λ t A t = 500 e – (0.246 / day) (2 days) A t = 500 e –0.49 A t = 500 x 0.612 A t = 306 uCi

31. IQBAL‘S COLLECTION Lecture 7 NUMERICAL-2 At 11:00 am of a rainy day ; 99mTc was measured 9mCi (333 MBq ). What was the activity at 0800 hrs on the same day. NUMERICAL-2 Step 1: Collection of Data A o = ? A t = 9 mCi T 1/2 = 6 hrs Elapsed time t = 3 hrs

32. Radionuclide Decay Terms and Relationships Lecture 7 NUMERICAL-2 Step 2: Look at the Units time t and half life should be in same unit. Pick the relevant equation N = N o / 2 n λ = 0.693 / T 1/2 A t = A o e – λ t NUMERICAL-2 Step 3: March towards Solution λ = 0.693 / T 1/2 λ = 0.693 / 6 = 0.1155 / day A t = A o e – λ t 9 = A o e – (0.1155 ) (3) 9 = A o e –0.3465 A o = 9 x 1.414 A t = 12.72 mCi

33. Radionuclide Decay Terms and Relationships Lecture 7 NUMERICAL-3 There is an activity of 360 mCi in 10 ml of a certain radioactive material. What will be its strength after two half lives in 2 ml? NUMERICAL-2 Step 2: Look at the Units time t and half life should be in same unit. Pick the relevant equation N = N o / 2 n λ = 0.693 / T 1/2 A t = A o e – λ t NUMERICAL-2 Step 3: March towards Solution N = N o / 2 n 90 mCi in 10 ml 18 mCi in 2 ml

34. Radionuclide Decay Terms and Relationships Lecture 7 NUMERICAL-4 On Monday at 0800 hrs a sample of I-131 is calibrated for 120 mCi in 20 ml. What will be activity at 1400 hrs on the same day and what will be the volume? Half life of I-131 is 8 days? NUMERICAL-5 At some point in time a source has an activity of 1000mCi. At a later point in time the activity is 62.5 mCi. The half-life is unknown. How many half lives have elapsed?

35. RADIOACTIVITY & NUCLEAR TRANSFORMATION Lecture 7 Be less curious about people and more curious about ideas.