Problem

The $\beta^{-}$ particles emitted in the decay of…

03:35

Problem 57 Hard Difficulty

Natural uranium is 0.7200$\%_{6}^{235} \mathrm{U}$ and 99.27$\%^{238} \mathrm{U}$ What were the percentages of $^{235} \mathrm{U}$ and $^{238} \mathrm{U}$ in natural uranium when Earth formed $4.5 \times 10^{9}$ years ago?

Answer

Hence percentage of 23 $\mathrm{U}$ at the time of earth formed is $23 \% $ and $23 \mathrm{U}$ is $177 \%$

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Physics 103

College Physics for AP® Courses

Chapter 31

Radioactivity and Nuclear Physics

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Video Transcript

Well, the current abundance of uranium 2 35 Um, look around. Abundance of uranium 2 25 of London's well, I uranium 2 35 um is equal to zero point 7 to 0 mosquito percent. So P stands for worsened Asia. And similarly, uh, the current abundance off uranium to 38 uranium 2 38 You crime. So Pete stands for a person. Teach S o B prime for getting him to 38 is equal to 99 point 27% too. 7%. Well, half life of uranium 2 35 So uranium 2 25 half life Half life is equal to seven. Multiplied by 10 to the power eat years and pop life of uranium poetry. It half life of uranium to 38 is equal to 4.5. Multiply by 10 to the dollar. Nine. Do you let the total current number off the uranium atoms in the certain sample be and 100 times and so the total the total got into number grunt number, uh, number move uranium. It comes in a certain sample. It tones in a certain sample certain sample be 100 times and then the current number of uranium. 2 35 items in the sample will pick you. And bye small end is equal to 0.72 Zito zero times. And so this end is the number of uranium 2 35 barons. So it's, uh, number. Oh, uranium 2 35 Adams in the sample. Okay. And the current number of uranium do 28 atoms in the sample will be, uh, n prime is equal. Do 99 point do seven times. And so this is the number number off uranium to 38 tones in the sample Now, therefore, the number of items off uranium 2 35 now, uh, the number. Uranium 2 35 Time T is equal to 4.5. Multiply by 10 to the power mine. Here you go can be given by can be you and bye and not is equal to end times e to the power tee times Eleanor too divided by half Life which equals 4.5 4.5 multiplied by tend to the barber nine years wanted by by Eleanor too. Divided by seven multiplied by 10 to the power eat years. Okay, so and not and not is equal. Do zero point 72 00 times and multiply by e, um, and and not is approximately equal to so and not is approximately equal to 62 point from zero to times and and the number of atoms of uranium 2 38 So number well Adams off uranium do 38. Time T is equal to 4.5, multiplied by 10 to the power nine years ago. Can be given by and not a crime and not prime is equal to end prime times e to the dollar are tee times half life Sorry tee times Eleanor do divided by half life and we have 4.5 Multiply by 10 to the power nine year dusty multiply by Eleanor too Divided by half Life is ah seven multiplied by 10 to the power eight years dude years and and not crime is equal to 99. Our point do seven times and multiply by e and not a crime is approximately equal to 1 98 going to five times. And now then for, uh, the abundance of uranium 2 35 So abundance of uranium 2 35 abundance. Oh, uranium 2 35 4.5, multiplied by 10 to the power nine year ago is given by be not is equal to and not divided by and not less and not prime. Multiply by 100 percent on this is equal to ah and not is 62.1 times and divided by, um then we have and not again 62.1 times and our place and not prime and not crime is 1 98 1 98.5 times and and hence be not is equal to 23 point 81 percent. So be not which is the abundance off uranium 2 35 Ford went fight multiplied by 10 to the power nine years ago is 23.81% Okay similarly for uranium to 38 So for uranium to 38 its abundance will be, ah be not prime Be not prime is ical toe and not crime divided by and not bless and not prime multiply by 100% and substituting values be not crime is equal to 62 point 02 times and divided by ah 62.2 times and bless and not prime is 1 98 fined five times and multiply by 100% and therefore be not crime is approximately equal to 7 to 6.19%.

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