Meteorite composition question

I know I'm probably only asking a small percentage of TTers out there, but the question stands:

Uranium 235 decays via a number of steps to lead 206 with a half life of 4.5billion years. The Solar system is 4.55billion years old. Approx how many lead nuclei are found for every uranium nuclei in meteorites?

U235 has 92 protons and 143 neutrons

PB206 has 82 neutrons and 124 protons

Er, I'd say there were equal proportions 50-50 surely? Assuming the meteorite was formed at the same time as the solar system, and that the uranium was evenly distributed within the meteorite so a disproportionate amount of uranium or lead wasn't knocked off during a collision with another meteorite. And assuming that the half-life's of intermediate products are comparatively minute.

The number of neutrons and protons is immaterial isn't it? We're just counting nuclei. Half-life is the statistical probability that in 4.5 billion years half of the lead nuclei have been converted to an equal number of lead nuclei. Or am I missing something?

I'm not sure to what level of detail the answer has to be developed but as an approx. I would go with the above. In detail the answer would be derived as follows -
Calculate decay constant = L = ln2 / THL
where THL = half life time (4.5 billion years)

then present number of molecules of U235 = N = No(e^(-L.t))
where No = original number of molecules of U235 and t = time (4.55 billion years)

Thus molecules of lead = NPb = NoPb + (No - N)
where NoPb = the original number of molecules of lead present in the meteorite (= 0 - I presume)
No = original number of molecules of U235
N is calc from above
"deduce" that for each molecule of U235 1 molecule of Pb is formed.

So if there were originally 1000 U235 there will be 496 now and thus 504 Pb206 - hence for every U235 there will be 1.015 Pb...

But the half life of U235 is 700 million years.

Wow! Thanks. Will pass on the answers. My head hurts just reading the question.

I would argue as above that the protons and neutrons are irrelevant in the equation as assumptions have to be made that the spread is equal unless there are other factors that determine the attraction between the 2 particles mentioned ?

Yes, I was going to say that.

I think the protons are given for the student to "deduce" that you can only get 1 molecule of lead from 1 molecule of U235, with some stuff left over...

Problem 1: U²³⁵ has a half-life of around 700M years; 4.5billion is the half-life of U²³⁸. Big difference between the two.
Problem 2: U²³⁵ decays to Pb²⁰⁶; again there's been a mix-up with U²³⁸.
Problem 3: There's an assumption that the decay is one-to-one. Many Uranium atoms will split into smaller shit like bismuth and cadmium, bypassing the "standard" decay.

woof.

Again, thanks. I'll copy & paste that as I have no chance of remembering it.