Radioactivity and nuclear transformation
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Transcript of Radioactivity and nuclear transformation
Lecture 7: May, 12, 2014
Shahid Younas
RADIOACTIVITY & NUCLEAR TRANSFORMATION
INTRODUCTION
Lecture 7
Radioactivity burst into the world without warning.
INTRODUCTION
Lecture 7
Antoine-Henri Becquerel
Director of Paris Museum of Natural
History
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.
INTRODUCTION
Lecture 7
Do you know why Uranium was given this name?
After the name of newly discovered planet Uranus in those
days.
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.
INTRODUCTION
Lecture 7
Silvanus P. Thompson- a British Electrical Engineer.
Uranium compound gave off invisible rays.
Hyper-phosphorescence
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.
INTRODUCTION
Lecture 7
Do you know what is the half life of Uranium?
U-238 : 447 Billion Years
U-235: 704 Million Years
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.
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
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”.
Radioactivity
Lecture 7
Process of spontaneous decay and
transformation of unstable atomic
nuclei accompanied with the emission
of nuclear particles and/or nuclear
radiation.
Radioactivity
Lecture 7
Henri worked on Uranium. Do you know on which source Madam
Curie worked?
Radium
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.
Radionuclide Decay Terms and Relationships
Lecture 7
Activity
Tradition unit is Curie (Ci)
1 µ Ci = 2.22 x 106dpm
S.I. unit is Becquerel (Bq)
Becquerel is one disintegration per second (dps)
Radionuclide Decay Terms and Relationships
Lecture 7
Do you know the relation between Henry Becquerel and Curie?
a. Henry was cousin of Curie.
b. Curie and Henry studied same high school
c. Henry and Curie shared first noble prize.
d. 1 milli Curie = 37 MBq
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
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 = λN
Decay constant is characteristic of each radionuclide.
Radionuclide Decay Terms and Relationships
Lecture 7
Decay constant for 99Mo is 0.252 per day.
Do you know the decay constant for technetium-99m?
0.115 per hour
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 = No / 2n
N is number of radioactive atoms remaining
No is the initial number of radioactive atoms
n is the number of half lives.
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.
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 / T1/2
Radionuclide Decay Terms and Relationships
Lecture 7
If we mix 99mTc and 131I with each other. How would you find
the decay of the mixture?
Mixture Rule or otherwise count for the longest half life
Radionuclide Decay Terms and Relationships
Lecture 7
Physical Half Life & Decay Constant
Radionuclide Symbol T 1/2
λ
Fluorine 18F 110 m 0.0063 / m
Technetium 99mTc 6.02 hrs 0.1151/ hr
Iodine 131I 8.02 d 0.0864 / d
Thallium 201Tl 3.04 d 0.2281/d
Gallium 67Ga 3.26 d 0.2126 / d
Iodine 125I 59.41 d 0.0117 / d
Radionuclide Decay Terms and Relationships
Lecture 7
Fundamental Decay Equation:
Decay constant and physical half life are related as;
Nt = No e - λt
or
At = Ao e - λt
Radionuclide Decay Terms and Relationships
Lecture 7
Physical Half Life:
Nt = number of radioactive atoms at time t
At= activity at time t
No = initial number of radioactive atoms
Ao= initial activity
e = base of natural logarithm
λ = decay constant
t = time
Radionuclide Decay Terms and Relationships
Lecture 7
NUMERICALS
A nuclear medicine technologist injects a patient with 500 µCi of
indium-111 labeled autologous platelets (T1/2 = 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?
Radionuclide Decay Terms and Relationships
Lecture 7
NUMERICAL-1
Step 1: Collection of Data
Ao = 500 uCi
T1/2 = 2.82 days
t = 48 hrs
At = ?
NUMERICAL-1
Step 2: Look at the Units
time t and half life should be in
same unit.
Pick the relevant equation
N = No / 2n
λ = 0.693 / T1/2
At = Ao e – λt
Radionuclide Decay Terms and Relationships
Lecture 7
NUMERICAL-1
Step 3: March towards Solution
λ = 0.693 / T1/2
λ = 0.693 / 2.82 = 0.246 / day
At = Ao e – λt
At = 500 e – (0.246 / day) (2 days)
At = 500 e –0.49
At = 500 x 0.612
At = 306 uCi
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
Ao = ?
At = 9 mCi
T1/2 = 6 hrs
Elapsed time t = 3 hrs
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 = No / 2n
λ = 0.693 / T1/2
At = Ao e – λt
NUMERICAL-2
Step 3: March towards Solution
λ = 0.693 / T1/2
λ = 0.693 / 6 = 0.1155 / day
At = Ao e – λt
9 = Ao e – (0.1155 ) (3)
9 = Ao e –0.3465
Ao = 9 x 1.414
At = 12.72 mCi
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 = No / 2n
λ = 0.693 / T1/2
At = Ao e – λt
NUMERICAL-2
Step 3: March towards Solution
N = No / 2n
90 mCi in 10 ml
18 mCi in 2 ml
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?
RADIOACTIVITY & NUCLEAR TRANSFORMATION
Lecture 7
Be less curious
about people and
more curious about
ideas.