Application of Thermal Technologies for Processing of Radioactive
Application Of Calculus in Radioactive
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Transcript of Application Of Calculus in Radioactive
Application Of Calculus in RadioactivePrepared by :
Ng Seng Wei D20091035105
Nor ‘Awaathif Bt Mohd Ghazali Lee
D20091035070
Words Of The Day
• Radioactive Decay Law
• Decay Constant
• Half-Life
APPLICATION OF CALCULUS IN RADIOACTIVE
RADIOACTIVE DECAY LAW
λt0t eNN
Let us say that in a sample of radioactive material there are N nuclei which have not decayed at a certain time, t. Therefore, we can say that the number which will decay depends on total number of nuclei, N and also the length of the brief period of time. In other words the more nuclei there are the more will decay and the longer the time period the more nuclei will decay. Let us donate the number which will have decayed as dN and the small time interval as dt.
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
dtNdN
t
0
N
N
dtNdNt
0
2. Secondly, we used calculus relationship of
tNNln0
t
3. Thirdly, we used the definition of logarithms
tNNln0
t
t
0
t eNN
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
2NN 0
t
21tt
Therefore the equation of Radioactive Decay Law could be rewrite by substituting and t.tN
21
21
21
t1
t
t
00
e2
e21
eN2N
21
21
21
21
21
1
t693.0
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
THANK YOU