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.

 

[rwisz]

I can provide some guidance to help answer these questions. Firstly, for measuring the half-life of an element, you would need a few instruments such as a stopwatch, a radioactive source, a detector, and a counting device. You would measure the time it takes for the number of atoms in the sample to decrease by half, and this value would be the half-life. The result you would get would be an approximate value, as it is difficult to measure the exact moment when half of the atoms have decayed.

For checking the radioactivity of objects, a Geiger counter is a suitable instrument as it can detect and measure the amount of radiation emitted by the object. The value you would measure is the radiation count, which would indicate the level of radioactivity. Again, this would give an approximate result as it is affected by factors such as background radiation.

The radioactivity decay law is based on the law of large numbers, which states that the larger the sample size, the more accurate the results will be. Therefore, it is not reliable to use with a small number of atoms as the results would not be statistically significant.

In regards to the carbon-14 dating question, you are on the right track. The equation you have mentioned is correct, and the value for T is indeed 5730 years. However, to determine the age of the bone, you would also need to know the initial amount of carbon-14 in the bone. This can be estimated by comparing it to the amount of carbon-14 in a normal bone, as given in the question. By using the equation and the known values, you can solve for t, which would give you the age of the bone.

I hope this helps you better understand these concepts and helps you answer the questions on your test. Remember, it is important to have a good understanding of the principles and equations involved in nuclear physics, rather than just memorizing them. Good luck on your test!