Few questions about nuclear physics

[wg1337]

I have this test and there are few questions that I can't answer or don't know if I'm right.

1) You need to measure the half-life of some random element. What instruments do you need? What values you need to measure? What results you will probably get?
2) You need to check the radioactivity for some random objects. What instruments do you need? What values you need to measure? What results you will probably get?
3) Why can't we use the radioactivity decay law (probably meant the one that shows how many atoms decay in time) with small number of atoms?
4) About carbon-14 dating. It is said that 1 gram of a random bone has 2 decays in a minute. Normal bone has 16 decays per minute. What is the age of the bone?

1) I think of using very precise scales. Measure mass and wait until half of the mass is gone. So I simply need to measure mass and time. I will most probably get only aprox. results, because scales won't measure 1 or 2 atom mass.
2) I thinking to use greiger counter. If the meter makes sound more rapidly, then material is more radioactive. I will probably get also aprox. results because I need isolated room, because other objects in the room could give scintillations.
3) If my method using scales to measure half-life, then the problem also be with the precision of scales, few atoms could be missed, but a ton of atoms won't be missed so easily.
4) Here I actually don't know what to do. I thought to calculate how many atoms are in 1 gram of carbon-14 and then use some equation I found in my book - N=N(0) * e^(ln2*t/T)
N will be N(0) - 2 and N(0) will be atoms in 1 gram and t will be the time, also T is a constant (not given, but maybe I should know it anyway), book says T is 5730 years. But this leaves out data about normal bone, so probably I'm thinking wrong :(

P.S. I hope my post won't be deleted because I didn't use the template.

 

[chaoseverlasting]

1. This is incorrect. When the element decomposes, it will decompose into another (stable) element. The masses of the two will be very close together with the difference being a couple of alpha or beta particles. This means, that your mass will remain almost constant, so you will never have the mass reduce by half.

2. Specifically, you would need to measure the alpha, beta and gamma particles emitted. I think you're right about a greiger counter, but perhaps your professor is looking for a more precise answer.

3. I'm not sure, but I think you're right here. Also, because it would take a really really long time to measure the decay of a few particles as compared to a few hundred. Say the half life of a material is 100 years and there are 4 atoms present. For two atoms to change, it would take a hundred years. To measure the change over such a long period of time is cumbersome to say the least.

4. You've used the right law. When they tell you that normal bone has 14 decays per minute, they are giving you the decay constant. Now, the law requires the initial number of atoms and the decay constant.

The form of the law that you've used here represents the decay constant $$\lambda =\frac{ln2}{T}$$. And you're missing a -ive sign in your expression.

If you differentiate the equation, you get $$\frac{-dN}{dt}=\lambda N$$

Your current decay rate is 2 decays per minute. This is your dN/dt. From this, you can get your current concentration of carbon atoms in the bone, N.

Substitute that value of N into the equation and find out the total number of carbon atoms in 1gm of the bone. The number of carbon atoms in 1gm is your No. Now, you can find the age of the bone by solving for t.

 

[SteamKing]

It's a Geiger counter, not greiger counter. (J.W. Geiger 1882-1945)

 

[wg1337]

1) So what can I do to measure? I thought that alpha and beta particles shoot out at high speed and the mass simply fly away, but I do see problems with it. Then I thought burning it, but there is a big chance that the new material also will burn. So out of ideas.

2) He won't mind, he needs something inside an empty field :P

4) Weird, I got that the bone is 200,000 years old, wasn't the dating method only available up to 65,000 years? I calculated how many decays are in a year, 2*365*24*60, but not sure if I can do that. If I calculated half-life as minutes, then my calculator went crazy, said that t = 0.