Particular nuclide to become half its initial value

[_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!

 

[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

 

[_Mayday_]

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

 

[rock.freak667]

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

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

 

[_Mayday_]

Ok, I understand the first bit, about picking the activity and then seeing what time it correspnds to. But I don't 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?

 

[rock.freak667]

But I don't 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?

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

And how do i calculate the activity?

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 $A=a_1-a_0$.

 

[_Mayday_]

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 $A=a_1-a_0$.

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??

 

[rock.freak667]

Is the activity simply the number of counts??

Yes, I believe so.

 

[_Mayday_]

Thanks, I understand now!