Nuclear Decay Problem: 238U to 206Pb & Atom's Age

[pattiecake]

The question is: Assume an atom just became Lead-206--why would such an assumption be important?--when it was orginally Uranium-238. Show all the steps it took to get from 238U to 206Pb. For each step, indicate the nature of the decay. Assume also that it spent exactly 1 half-life as each of the intermediate isotopes. Finally, how old is this atom?

I'm working on an assignment that's not due for awhile, and being we just started our inorganic chem. course, I really don't understand the major concepts here at all. Not that I'm asking anyone to do my homework here, but maybe you can start me off with some things I'm confused on, like...

1) What initiates decay?
2) How do you know how many particles the atom gives off at one time? (i.e. hydrogen vs. helium)
3) How the heck do you know what kind of energy it will give off?

 

[arivero]

1)Decay is initiated randomly, controlled by the half-life, lifetime, or mean life parameters.
2)the same parameter tells you how many by unit of time; that is probability.
3)the mass difference becomes energy

 

[pattiecake]

Hi Arivero, thanks for your response!

Given what you've told me...we have 238Ur-->Th + ?

How can I determine the probability of what is going to happen, and use that to complete the reaction?

 

[Astronuc]

There are two types of decay mode for radioisotopes between Pb and U,

beta decay and alpha decay.

In beta decay, a nucleus emits a beta particle (electron, e[sup-[/sup]) and an antineutrino (neutral and very low mass), but the important thing is that the atomic mass (number of nucleons) does not change, but the atomic number (Z) increases by 1.

In alpha decay, a nuclear emits an alpha particle (nucleus of ₂He⁴), and so the atomic mass decreases by 4 and the atomic number by 2.

So ₉₂U²³⁸ --> ₉₀Th²³⁴ + ₂He⁴

This may be of use with your problem

http://wwwndc.tokai.jaeri.go.jp/CN04/

 

[pattiecake]

Thanks Astronuc...btw, where is Uluru?

So does the atom just keep emitting an alpha particle until it reaches the atomic number corresponding to lead? Shouldn't there be something more complicated here?

 

[Astronuc]

http://www.worldwindcentral.com/hotspots/view_hotspot.php?id=446 is in the heart of Australia - Latitude : -25.3742, Longitude : 131.037

See also - Uluru at sunset

Actually, I live not too far from Pittsburgh, just north of NYC.

So does the atom just keep emitting an alpha particle until it reaches the atomic number corresponding to lead? Shouldn't there be something more complicated here?

Yes, it's a little more complicated, because some radionuclides emit beta particles.

See U²³⁸ decay scheme at - http://hyperphysics.phy-astr.gsu.edu/hbase/nuclear/radser.html#c3

Isotopes of At, Rn, Bi and Po may have dual mode decay either alpha or beta, but only one occurs.

 

[NEOclassic]

Or more completely, I think!

There are two types of decay mode for radioisotopes between Pb and U, beta decay and alpha decay.

So ₉₂U²³⁸ --> ₉₀Th²³⁴ + ₂He⁴

U-238 - alpha --> Th-234 - beta --> Pa-234 - beta --> U-234 - alpha -->
Th-230 - alpha --> RA-226 - alpha --> Rn-222 - alpha --> Po-218 - alpha
--> Pb-214 - beta --> Bi-214 - beta --> Po-214 - alpha --> Pb-210 - beta
--> Bi-210 - beta --> Po-210 - alpha --> Pb-206 <-- Tl-205 + neutron

Cheers, Jim

 

[pattiecake]

Thanks everyone for your help...

I'm still not seeing how Th234 emits a beta particle. Can't it just emit an alpha, bringing us to 230Ra? What does it emit a beta, what factors control this?

 

[Astronuc]

Radioactive decay of a nucleus is a stochastic phenomenon. One cannot determine when a particular nucleus will decay, and if there are two possible modes, by which mode it will decay. That's one of the natural mysteries.

We do know that if we have a large population of a radionuclide, after one half-life, approximately one-half of that population will have decayed.

Let me dig around to see if I can find some additional information on the choice of decay modes.