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When we plot the amount of radioactive nuclei at certain time intervals, we get a plot like this:

enter image description here

First of all, what kind of function is this? To me it looks like $y=(e^x)^{-1}$ or $y=(\log x)^{-1} $ (the part in the first quadrant of course).

Secondly, what is the best way to go about making such a graph for an isotope with a really short half life? I believe my textbook uses a logarithmic scale on the y-axis, but could you also just take the log of every data you get? And it doesn't matter which base you log has right, except that it must be the same for every piece of data, to create a straight line?

Ylyk Coitus
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1 Answers1

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a) The equation for half life can be written as:

$$y = \left(\dfrac12\right)^{t/h}$$

t is the time elapsed;

h is the half life (time for 1 unit to become half);

y is the amount left at any time t.

b) I don't quite get your second question, but if I got it right, you can plot the log of the amount left against the time to get a straight line like this:

$$\log(y) = \dfrac{t}{h} \log\left(\dfrac12\right)$$

Jerry
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  • I meant what the name of such a function is – Ylyk Coitus Apr 07 '13 at 11:01
  • @YlykCoitus: There is no specific name for this. You can just say the graph is SIMILAR to such a function, but it is not the same as any. – Inceptio Apr 07 '13 at 11:05
  • @YlykCoitus A half life function? I'm not too good with how functions are called ._. Oh and for your second question, you can take the log of the amount of nuclei left against the time. I'll add that to the above. – Jerry Apr 07 '13 at 11:06
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    @YlykCoitus I think you could call it a decaying exponential function. – Sam Apr 07 '13 at 11:53