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A nuclear physicist finds 1.0$\mu \mathrm{g}$ of $^{236} \mathrm{U}$ in a piece of uranium ore and assumes it is primordial since its half-life is $2.3 \times 10^{7} \mathrm{y} .$ (a) Calculate the amount of $^{236} \mathrm{U}$ that would had to have been on Earth when it formed $4.5 \times 10^{9}$ y ago for 1.0$\mu \mathrm{g}$ to be left today. (b) What is unreasonable about this result? (c) What assumption is responsible?
a) $7.7 \times 10^{49} \mathrm{kg}$b) The initial mass of the Uranium is extremely large that seems unreasonable because thatmuch mass is even greater than the entire Milky Way galaxy.c) The assumed half life is very small and hence responsible for the unreasonable result. Thehalf life of the U-236 must be larger than the assumed value.
Physics 103
Chapter 31
Radioactivity and Nuclear Physics
Nuclear Physics
Cornell University
University of Sheffield
McMaster University
Lectures
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Hi friends here it is given in the uranium or uranium to 36 mass off uranium to 36 is 10 Micrografx. If half life off uranium to 36 is 2.3 in tow, 10 to the power seven years. We have to calculate initial mass off uranium to 36 before 4.5 in tow. 10 to the power nine years. What is unreasonable about this region? But a Jensen is responsible. This is the problem based on radio activity. Mass off the reductive material left after 30 seconds is given by AM is going toe am not exponential off minus Landon Toti on Dhere Lambda having the value 0.693 upon t half so from equation Bannon to initial must am not committed in its and into exponential off 0.693 d Divided by T hop. Now substituting the value mass is given but microgram that is one in tow. 10 to the power minus nine Caijing Explanation off minus 0.6 and 93 Time is given 4.5 and tow 10 to the bubble. Nine upon half life is 2.3 and tow 10 to the power seven. So on solving it. Initial moss off uranium to 36 people. Get 7.7 and tow 10 to the power 49 kg B. But the initial must. It's a very height that is on a reasonable see the half. Life is taken very smart, that's all. Thanks for watching it.
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