# Can you find out the date of a radioactive material wothout

1. Aug 25, 2010

### iceveela

You have 100 grams of radioactive material, how do i know the half life and the time

i have 100 grams of material X.

you do not know the half-life
you do not know the time it started to decay

what is its half-life/starting time?

is this equation even solvable? if so, how?

2. Aug 25, 2010

### QuantumPion

Re: how can you date a radioactive substance if you are missing...

The half-lives of radioisotopes are well-known, you can look them up online in wikipedia for example.

For carbon-14 dating, organic material obtains an equilibrium concentration of carbon-14 equal to the concentration in the atmosphere (created by radiation from space). Once the material is dead and buried, no more new carbon-14 is accumulated and the exponential decay begins. Knowing the half-life of carbon-14, the amount of carbon-14 in the atmosphere (which is fairly constant except for the recent period of atmospheric nuclear weapons testing) and the current concentration, you can calculate the age of the material with the following equation:

$$N(t) = N_0 e^{\lambda t}$$

$$t = \frac{1}{\lambda} ln \frac{N}{N_0}$$

Last edited: Aug 25, 2010
3. Aug 25, 2010

### iceveela

Re: how can you date a radioactive substance if you are missing...

sounds nice but i do not know what radioactive material X is, i have never seen it before...

4. Aug 25, 2010

### QuantumPion

Re: how can you date a radioactive substance if you are missing...

It is possible to determine what isotope a radioactive substance is by measuring the type and energy of the emission and comparing its spectrum to a known database. You need the right equipment and software to do this though.

5. Aug 25, 2010

### iceveela

Re: how can you date a radioactive substance if you are missing...

if this was a brand new material not known to man, how could i do it?

6. Aug 25, 2010

### QuantumPion

Re: how can you date a radioactive substance if you are missing...

I may be wrong about this but I'm pretty sure the half-lives of all radioactive isotopes are known, with the exception of extremely unstable and short-lived isotopes (which you could not use for dating anyway). You can see the chart here: http://www.nndc.bnl.gov/chart/

7. Aug 25, 2010

### omrihar

Re: how can you date a radioactive substance if you are missing...

The decay of a radioactive material is a process without memory - it means that the decay would look the same no matter how "old" the material is.
If you have 100 grams of this material, you define this as $$N_0$$ in the equation quoted above. If you want to find the half-life you should measure the amount you have left after a certain amount of time and then you can find out $$\lambda$$.

Without any further knowledge, you cannot use this material for dating. The way radioactive materials can be used for dating is by the additional knowledge of their abundance at a given time. If you know what $$N_0$$ was at some time in the past, and you know how much you have left, then knowing the half-life of the material allows you to calculate the time that has passed.

Hope this helps...

8. Aug 25, 2010

### iceveela

Re: how can you date a radioactive substance if you are missing...

umm... so dating is calculated by the assumption that we already know the half-life? and no equation exist that can bring us to the half-life or decay starting time without either the half-life or the decay starting time?

i am confused!!!

9. Aug 25, 2010

### Integral

Staff Emeritus
Re: how can you date a radioactive substance if you are missing...

Nothing that a good course in Quantum Mechanics wouldn't cure.

10. Aug 25, 2010

### omrihar

Re: how can you date a radioactive substance if you are missing...

iceveela - i think it would be helpful if you tried to explain again what exactly you know, and what you want to find out.

The lifetime (or half-life which is simply the lifetime multiplied by a constant) is a property of the radioactive substance. If you do not know anything about the substance, except that it is radioactive and that it weights 100gr, you cannot tell anything more by it.

If you know more, then please tell us what it is and we can go on...

11. Aug 25, 2010

### QuantumPion

Re: how can you date a radioactive substance if you are missing...

Radioactive dating uses some assumption about the concentration of a particular isotope in the past and compares its concentration to the present, using its known rate of decay (half-life).

If you had an unknown sample containing two radioactive substances, one that decayed into the other, it might be possible to determine the age of the sample by measuring the ratio of concentrations between the two.

12. Aug 25, 2010

### krishna mohan

Hi..

Half-life is defined as the time required for the radioactive material to decay to half its initial value.....The initial value means the value at the time you started observing...

If you have 100 gms left...then half-life is the time when you have 50 grams left...

Experimentally, you would have a detector which measures radioactivity....You measure radio activity at time t1...then wait for the radioactivity to become half the value you started with...note the time as t2.....and your half-life is t2-t1...

It does not matter when you start your observation...

13. Aug 25, 2010

### QuantumPion

Re: how can you date a radioactive substance if you are missing...

Not at all, this is Chemistry 101 really.

14. Aug 25, 2010

### HallsofIvy

Re: how can you date a radioactive substance if you are missing...

If you do not know the half-life apriori, you will have to determine it by experiment- that is, measure the amount of radioactive substance now, wait at while (the longer you wait (the more accurate you result) and measure the amount now. Taking "t" to be the time you waited and "T" to be the unknown half line, A(0) to be the amount you first measured and A(t) to be the amount you measured at time t, you have
$$\left(\frac{1}{2}\right)^{t/T}= \frac{A(t)}{A(0)}$$.

You know t, A(0), and A(t) so you can solve for T.

Once you know T, you can then solve the problem you were given.

15. Aug 25, 2010

### iceveela

Re: how can you date a radioactive substance if you are missing...

ok, you guys are confusing me, in order to find out what "λ" is you need the half-life or the initial decay starting time...

"The decay constant (λ) of radioactive decay is equal to the reciprocal value of the average lifetime (τ). Between the decay constant, the average lifetime, and the half-life (T½) the following relations exist:

λ = τ -1 = T½-1 · ln 2 "

and in order to find that out, you need to know at least the half-life or the initial time. but you cannot find that out until you know that "λ" is...

ahhhhh!!!!!!!

16. Aug 25, 2010

### Rajini

I guess you cannot solve, i.e. you wont get any numerical values with out using some e.g., detector and proportional counter.
Because solving your problem is same as solving two equations with more than 2 unknown quantities.

17. Aug 25, 2010

### TheRealTL

Re: how can you date a radioactive substance if you are missing...

You find the half life by measuring its mass....waiting....and then measuring its mass again. THEN CALCULATING.

18. Aug 25, 2010

### Janus

Staff Emeritus
Note, this thread has been merged with an identical thread from General Physics.

19. Aug 25, 2010

### iceveela

Re: how can you date a radioactive substance if you are missing...

how does this work with large-scale times like thorium 232, uranium 238 and Samarium-147, just "measuring the mass and waiting" will be highly inaccurate for these large-timescale rocks...besides, the decay rate is random...

20. Aug 25, 2010

### QuantumPion

Re: how can you date a radioactive substance if you are missing...

I think that would only work if the decay product happened to be a gas that escaped the sample! And even then it would be extremely difficult to quantify.

Generally the way to determine the half-life is to measure the activity of the sample over time. It will decay exponentially according the formula above.

The decay of any single nucleus is random, but the average decay rate for a very large number of atoms is not. Some isotopes have such long half-lives that they were until recently though to be stable, such as Bismuth-209. But for U-238 and others, even though they are long-lived isotopes, it is still not too difficult to measure their half-lives because of the scales involved (huge number of atoms).

21. Aug 25, 2010

### arivero

If it is long lived... you need the spectrum.

If it is short lived... forget, you have no a radiactive source anymore.

If it is mid-lived: measure the Intensity (power, watts, calorimeter, counter). Wait for the intensity to decrease to one half of the initial you have measured. This interval is the half live.

22. Aug 25, 2010

### iceveela

Re: how can you date a radioactive substance if you are missing...

so the atom is not random if it is in large quantities? so by what you say, it is not inaccurate to measure something this way based on the assumption that the short lived radioactive materials are no different in randomness as ones that can take several billions of years. so it should be accurate to measure the difference in a certain time period and date that small difference in the material back several billion or trillion years?

this does not seem scientific to me, it sounds like it is based on estimates. (if 100 grams of uranium 238 loses .0000004 grams of mass because of decay in a time-frame of 2 years, thus, it should be OK to say that this tiny fragment can be traced back to 4.5 billion years) that does not seem like science to me. unless you know for a fact that this number is constant throughout time, which of course, with large scale decay, we really do not know...

so why say it is constant when we really do not know that it is?

23. Aug 25, 2010

### krishna mohan

I am a little confused about what exactly is the question....

Let me rephrase the question and please let us know if this is what you wanted...

Someone presented you with 100 gms of a radioactive material...he or she has not given you any information about the material...what it is or where it was obtained from etc...

..you want to find its decay constant and half-life.....you are allowed to do any experiment you want.....so how will you do it?

24. Aug 25, 2010

### iceveela

the question is: i have 100 grams of a unknown substance, i do not have the half life or the starting decay time. i need to accurately measure the half-life and the starting decay time. i am NOT allowed to just take a sample over a time frame and backtrack it as i cannot base it on assumptions that it was always constant. or any other assumptions...

how do i find the half-life/decay starting time?

25. Aug 25, 2010

### QuantumPion

There is no physical "decay starting time" as you have phrased it. Radioactive isotopes are always decaying.

You can determine the half-life by measuring the activity now and some time t later and solve for lambda in the equation above.

Half lives are fundamental properties of particular isotopes and do not change over time (as far as we know). If you measure what the half-life is now you know what it was a billion years ago.

You can only determine how old the sample is based on how far your assumptions about its history go. If you can't make any assumptions then you cannot make any determination about its age.