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Theory of Radioactive decay

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Introduction

Theory of Radioactive decay

1st consider an analogous model.

In the dice analogy of radioactive decay, the number of dice which decayed per throw (∆N) is given by

                ∆N = image01.pngN

                ∆ means a small change

                N is the total number of dice at start

The minus sign indicated that ∆N is ever decreasing and the image02.pngcomes from the probability that advice will show a six when thrown.

2nd – Now consider a real example of radioactive decay. In any such example, if k is the change of decay per second then in a time interval ∆t, a fraction k∆t will decay.

The “k∆t” term here is equivalent to the image10.png

...read more.

Middle

image24.png dt

Where Nimage07.png          = number of atoms at time t=0

Where N            = number of atoms at time t=t

image03.pngimage04.png        =image00.png

image03.pngimage05.png =        -kt

image06.png

image03.pngN = Nimage07.png. eimage08.png

Half life

This is the time taken for N to becomeimage09.png.

i.e. the number of atoms remaining after time t to become equal to half of the original number of atoms present.

...read more.

Conclusion

ity/15668/html/images/image11.png" style="width:41.33px;height:41.33px;margin-left:0px;margin-top:0px;" alt="image11.png" />eimage12.png

Taking log to the base e gives us:

timage13.png = image14.png

The activity of a radioactive material

This is exactly the same thing as its rate of decay. Radioactive sources are marked with “strengths” or activities in curies 1 Curie = 3.7*10image15.png disintegrations per second. OR nowadays in Bequerels 1Bq = 1 disintegration per second.

Since activity = rate of decay.

        A = image17.png

And since

        N = Nimage07.pngeimage08.png

        A = image18.png

image03.pngA = -kNimage07.pngeimage08.png

But

        N = Nimage07.pngeimage08.png

image03.pngA = -kN

By the use of substitution we come get the following equation.

image20.png A = Aimage07.pngeimage08.png

...read more.

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