Uranium has a half life of 704000000. A sample was found to have 10g of Uranium-233 and 70g of the daughter element. What percentage is remaining?

Answer 1

Hi Connor N.,

Sorry, but your question is a mess! First of all, your quoted half-life needs time units on it. You seem to be referring to U235, which has ~700 million years as a half-life.

Next, you need info as to what "daughter element" refers to. I suggest you look up (copy this address, then remove all the spaces, before you click on it -- Wyzant won't allow direct links!) htt ps : / / www. nrc. gov/ docs/ ML1122/ ML11227A233 . pdf

You will notice that the U235 decay chain ends in Pb207, which is considerably lighter than the starting U235! Therefore, you will need to correct for the amount of daughter found. Since this entire decay process is pretty quick, compared with the initial decay of U235 (note, not U233!), just multiply by 235/207, you end up with ~79.47 g. This is the quantity you need to compare with 10g of U235, as an exponential decay.

So, the equivalent starting mass (as units of %) would have been: 10 + 79.47 = 89.47 g.

As a ratio, ending:starting = 10/89.47 = 0.1118

This is (1/2) ⁿ = 0.1118 (This is one way of solving; you could also model through an exponential decay equation, but that's a little longer to do.)

Solve this by logs (the opposite operation of raising to an exponent):

log (1/2) ⁿ = log (0.1118)

n log (1/2) = -0.9517

n * (-0.3010) = - 0.9517

n = 3.17 . This is the number of half-lives that have elapsed.

So, years = 7.038*10^8 years * 3.17 =~ 2.26 *10^9 years

Please study the above math procedure; you'll need to do it lots more, both in physical science/chemistry and math courses!

-- Cheers, -- Mr. d.