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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

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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

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Do you know why Uranium was given this name?

After the name of newly discovered planet Uranus in those

days.

INTRODUCTION

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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

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Silvanus P. Thompson- a British Electrical Engineer.

Uranium compound gave off invisible rays.

Hyper-phosphorescence

INTRODUCTION

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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

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Do you know what is the half life of Uranium?

U-238 : 447 Billion Years

U-235: 704 Million Years

INTRODUCTION

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He tried to destroy Uranium’s power by dissolving and re-crystalizing to retain his philosophy of phosphorescence.

But

All in Vain.

INTRODUCTION

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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

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Henri worked on Uranium. Do you know on which source Madam

Curie worked?

Radium

Radionuclide Decay Terms and Relationships

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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.


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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)


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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


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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


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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.


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Decay constant for 99Mo is 0.252 per day.

Do you know the decay constant for technetium-99m?

0.115 per hour


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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.


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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.


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Physical Half Life:

Decay constant and physical half life are related as;

λ = ln 2 / T 1/2

λ = 0.693 / T1/2


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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


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


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Fundamental Decay Equation:

Decay constant and physical half life are related as;

Nt = No e - λt

or

At = Ao e - λt


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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


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?


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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


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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


Lecture 7

NUMERICAL-2


time t and half life should be in

same unit.


N = No / 2n

λ = 0.693 / T1/2

At = Ao e – λt

NUMERICAL-2


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


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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


time t and half life should be in same

unit.


N = No / 2n

λ = 0.693 / T1/2

At = Ao e – λt

NUMERICAL-2


N = No / 2n

90 mCi in 10 ml

18 mCi in 2 ml


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.

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