The half life of 235 U is 7.04*10 8 year and the half-life of 238 U in uranium o
ID: 1893902 • Letter: T
Question
The half life of 235U is 7.04*108 year and the half-life of 238U in uranium ore is 0.007.
a)Calculate the activity of 100g of pure 238U and 100g of pure 235U.
A theory of astrophysics states that all the heavy elements like uranium are formed in the interior of massive stars. When stars run out of nuclear fuel, they implode and then explode, releasing most of their matter into space. Elements heavier than iron are produced during the explosion.
b) Assuming that at the time of the explosion there were equal amounts of 235U and 238U, how long ago did the star explode that released the elements that formed Earth? Hint: take the time of the nova as t=0, when the ratio of the number of 235U to 238U was 1, and use the half life formulas to write the current ratio.
Explanation / Answer
the number of atoms is N = [100/238] (6.02 x 10^23 atoms) =2.53*10^23 atoms Hey i searched net and found that the half life for 238U is 4.468×10^9 years but in question you have mentioned 0.007 something i am not sure what it is. I am doing the numerical with the half life on net if you have some other value just replace it in place of lamda below the activity is given as N = [(0.693) / (1.41 x 10^17 s)] *N = 0.693/1.41*10^17 * 2.53*10^23 = 1243469.7 decays/sec ------------------------------------------------------------------------ Now for 235 U the number of atoms is N = [100/235] (6.02 x 10^23 atoms) =2.562*10^23 atoms the activity is given as N = [(0.693) / (0.22 x 10^17 s)] *N = 0.693/0.22*10^17 * 2.562*10^23 = 8070300 decays/sec the number of atoms is N = [100/235] (6.02 x 10^23 atoms) =2.562*10^23 atoms the activity is given as N = [(0.693) / (0.22 x 10^17 s)] *N = 0.693/0.22*10^17 * 2.562*10^23 = 8070300 decays/sec b) From the half life equations we have N(t) = No* exp(-t) So for U235 it is given as N1(t) = No * exp(-3.15*10^-17 * T)...................................1 For 238U N2(t) = No * exp(-0.491*10^-17 * T)...................................2 1 divided by 2 gives N1(t)/N2(t) = 0.007 = exp ( -3.15*10^-17 +0.491*10^-17)T -2.659*10^-17 T = ln(0.007) T = 1.866*10^17 secRelated Questions
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