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Problem 59 Easy Difficulty

The theory of nuclear astrophysics is that all the heavy elements like uranium are formed in the interior of massive stars. These stars eventually explode, releasing the elements into space. If we assume that at the time of explosion there were equal amounts of $^{235} \mathrm{U}$ and $^{238} \mathrm{U},$ how long ago were the elements that formed our Earth released, given that the present $^{235} \mathrm{U} /^{238} \mathrm{U}$ ratio is 0.007? (The half-lives of $^{235} \mathrm{U}$ and $^{238} \mathrm{U}$ are $0.70 \times$ $10^{9}$ yr and $4.47 \times 10^{9}$ yr, respectively.)

Answer

t=5.9 \times 10^{9} y r

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Top Physics 103 Educators
Andy C.

University of Michigan - Ann Arbor

LB
Liev B.

Numerade Educator

Marshall S.

University of Washington

Aspen F.

University of Sheffield

Video Transcript

question for solving for the boat. Constance, we get Lambda Uranium 2. 35. Well, he goes to I learned to divide by the house. Okay. And from here, after putting values, we get 9.9. My pleasure. We tend to the bottom. I understand one by ear that is here it was similarly Linda uranium 2. 38 will be equals to Ellen to everybody, which will come out to be 1.55 molecular weight into the Afghanistan here universe. So, no, we deduce that the uranium racial value U ratio is equal to 0.7 That is seven weight into the par minus three and which can be expressed as you ratio equals to a number of atoms of uranium 2. 35 developed a number of items of property. Eight uranium. Okay. And it will be close to a to the power minus lambda to 35 minus lambda 2 38. Butler by t. Now substituting the values, we can estimate the elapsed time from this regulation equals two minus of Ellen seven. Molecular weight into the power three. Divide by Lambda 2 35. Minus lambda 2 38 Okay, so now, substituting both the values in this situation to get equals two minus Ln seven manipulated by 10 to the power three. Developing Lambda to 35 is 9.9, multiplied by 10 to the power manage, Stan minus 1.55 multiplied by 10 to the power minus 10. Okay, so after solving this value minus three, this is actually minus three. Okay, so after solving this value, T comes out to be 5.9 multiplayer weight and to the power nine.

Top Physics 103 Educators
Andy C.

University of Michigan - Ann Arbor

LB
Liev B.

Numerade Educator

Marshall S.

University of Washington

Aspen F.

University of Sheffield