The Student Room Group

Hard Radioactivity Question.

The heaviest elements found on Earth were created in stellar explosions (supernovae). Assuming that all the uranium now found on Earth was created in a single supernova and that uranium-235 and uranium-238 were created in equal amounts, estimate the time since explosion occurred given the following data:

Observed relative abundance of Uranium-235 = 0.7%

Observed relative abundance of Uranium-238 = 99.3%

Mean lifetime of uranium-235 = 1.01 x 10^9 years

Mean lifetime of uranium-238 = 6.49 x 10^9 years



I dont know how to start off, any help will be greatly appreciated

Thanks!
Neo1
The heaviest elements found on Earth were created in stellar explosions (supernovae). Assuming that all the uranium now found on Earth was created in a single supernova and that uranium-235 and uranium-238 were created in equal amounts, estimate the time since explosion occurred given the following data:

Observed relative abundance of Uranium-235 = 0.7%

Observed relative abundance of Uranium-238 = 99.3%

Mean lifetime of uranium-235 = 1.01 x 10^9 years

Mean lifetime of uranium-238 = 6.49 x 10^9 years



I dont know how to start off, any help will be greatly appreciated

Thanks!


i think and i could be wrong you multiply (0.7 x 1.01 x 10^9) + (99.3 x 6.49 x 10^9) and divide all of that by 100

but i might be wrong
Reply 2
If you start off with 50% U -235 and end up with 0.7%, then you can apply the usual exponential decay law to work out the time needed. The half life of U-238 is longer and you can assume that the amount of U 238 will be approx constant.

Alternatively , plot the amounts given by exponentials on a spreadsheet and run it forward in time until you reach the desired proportions.
teachercol
If you start off with 50% U -235 and end up with 0.7%, then you can apply the usual exponential decay law to work out the time needed. The half life of U-238 is longer and you can assume that the amount of U 238 will be approx constant.

Alternatively , plot the amounts given by exponentials on a spreadsheet and run it forward in time until you reach the desired proportions.


and where are the half lifes in the question
goodbyeforever
and where are the half lifes in the question

half life is related to mean lifetime, there's only a factor of ln2 in it (I think).
Reply 5
F1 fanatic
half life is related to mean lifetime, there's only a factor of ln2 in it (I think).
Yes. τ=1/λt1/2=τln2.\tau = 1/\lambda \Rightarrow t_{1/2} = \tau \ln 2.

EDIT: τ\tau is the mean lifetime.
F1 fanatic
half life is related to mean lifetime, there's only a factor of ln2 in it (I think).


but for a AS question i think it is slightly beyound the level do you not think?
Reply 7
Its an A2 question
goodbyeforever
but for a AS question i think it is slightly beyound the level do you not think?

For A2? Not really, if you can deal with what an exponential is in a decay then you can deal with a factor of ln2, unless you meant the concept of radioactive decay in general which is a standard part of all A-level courses I think.
Reply 9
I have a solution in the spoiler (in case you are still working on it).

Spoiler