Particular nuclide to become half its initial value

1. Jan 27, 2008

_Mayday_

I know that half-life is the time taken for the activity of a particular nuclide to become half its initial value. But I do not understand the equation that I have "learned" relating to it.

$$T^{1/2} = \frac{0.69}{\lambda}$$

I am not sure what any of the letters of symbols stand for. I have looked them up, but they still don't make sense to me.

$$\lambda$$ = Decay Constant
$$0.69$$ = Natural Logarithm
$$T^{1/2}$$ = Half life?

Is the decay constant given? How would you go about finding the decay constant in an experiment with a Geiger Muller Counter and a radioactive source?

What does the natural Logarithm stand for or mean?

Sorry these are probably quite trivial questions, but I have looked and once I know what they are and why they are, I can work out in my mind how it works, and do soem firther work. Thanks!

2. Jan 27, 2008

rock.freak667

The number of nuclei present at time t is given by

$$N=N_0e^{-\lambda t}$$

When $t=T_{\frac{1}{2}},N=\frac{N_0}{2}$

Now when you sub that into the first equation and simplify you will get

$$T_{\frac{1}{2}}=\frac{ln2}{\lambda}$$

As for the experiment you could measure the count-rate(Activity) and then plot activity vs. time and then find the half-life then use the equation relating decay constant and half-life

Last edited: Jan 27, 2008
3. Jan 27, 2008

_Mayday_

How would I find the half life, using an activity vs. time graph?

4. Jan 27, 2008

rock.freak667

Choose some value for Activity(A), then find the time for that value of A, then find the time for A/2...then A/4 and so forth. Then find the average of those times and that is the half-life

5. Jan 27, 2008

_Mayday_

Ok, I understand the first bit, about picking the activity and then seeing what time it correspnds to. But I dont uderstand the A/2 and A/4 bit? Why is it A/2? Am I still just picking any activity and seeign what it corresponds to?

And how do i calculate the activity?

6. Jan 27, 2008

rock.freak667

No. The half-life is the time taken for the activity to fall to half of its initial value.

From the GM counter. Measure the background radiation first(Call this $a_0$). Then measure the activity from the radioactive source in some time intervals.(call this $a_1$). Then the activity at that time is given by $A=a_1-a_0$.

7. Jan 27, 2008

_Mayday_

Sorry about the first question, that is a common case of me not thinking

Ok using the GM counter how will i measure the activity? Is the activity simply the number of counts??

8. Jan 27, 2008

rock.freak667

Yes, I believe so.

9. Jan 27, 2008

_Mayday_

Thanks, I understand now!