Application Of Calculus in Radioactive

Prepared by :

Ng Seng Wei D20091035105

Nor ‘Awaathif Bt Mohd Ghazali Lee

D20091035070

Words Of The Day

• Radioactive Decay Law

• Decay Constant

• Half-Life

BEHIND THE SCENE OF RADIOACTIVE

1896 – Antoine Henri Becquerel – discovered by accident – Uranium wrapped in paper stored in dark – emit a penetrating radiation that can produce bright images on a photographic plate. Creates an electric discharge in air.

1898 – Marie Curie – thorium emit radiation – directly proportional to the concentration of the element in the mineral but to the nature of the compound . Radioactivity – unaffected by T, P or other physical and chemical condition

In 1903, Becquerel and the Curies together received the Nobel Prize in physics. This award was for their discovery of radioactivity and their other contributions in this area. Marie Curie received a second Nobel Prize in 1911 for the discovery of polonium and radium. She was the first person to win two Nobel Prizes. Did you know that the Curie's had a word named after them? That's right! The curie is a basic unit of measurement for describing radioactivity.

APPLICATION OF CALCULUS IN RADIOACTIVE

RADIOACTIVE DECAY LAW

λt0t eNN

How Calculus was Applied in It?

1. First we used integral calculus to figure out what was happening over a period of time by integrating what we knew could occur in a brief interval of time.

- dN α N.dt

- dN = λN.dt

NdtN

dN

t

0

N

N

dtN

dNt

0

2. Secondly, we used calculus relationship of

tN

Nln

0

t

3. Thirdly, we used the definition of logarithms

tN

Nln

0

t

t

0

t eN

N

t0t eNN

Until then it will form an equation of,

RadioactiveDecayLaw

The Radioactive Decay Law tells us that the number of radioactive nuclei will decrease with time in an exponential pattern with the rate of decrease being controlled by the decay constant. The law could be shown in graphical figure as below:

RELATIONSHIP BETWEEN RADIOACTIVE DECAY LAW AND

HALF-LIFEThe law tells us that at any time, t:

Meanwhile, the definition of half-life tells us that:

When

t0t eNN

2

NN 0t

21tt 21tt 21tt

21tt

Therefore the equation of Radioactive Decay Law could be rewrite by substituting and t.tN

21

21

21

t1

t

t

00

e2

e2

1

eN2

N

21

21

21

21

21

1

t

693.0

693.0t

t693.0

t2ln

t2ln

These last two equations express the relationship between the decay constant and the half-life

~Lets Try This !!~

QUESTION

THE END

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