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There is more than one isotope of natural uranium. If a researcher isolates 1.00 $\mathrm{mg}$ of the relatively scarce $^{235} \mathrm{U}$ and finds this mass to have an activity of $80.0 \mathrm{Bq},$ what is its half-life in years?

$\left[7.04 \times 10^{8} y\right]$

Physics 103

Chapter 31

Radioactivity and Nuclear Physics

Nuclear Physics

Rutgers, The State University of New Jersey

Simon Fraser University

University of Winnipeg

McMaster University

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the activity off a sample is given by are is equal to 0.693 times and divided by life. Ah, half life is on T by one by two just 1/2 Life And let's stop this equation for half life. So half life is equal to 0.69 pre, uh, times. And do you mind it by are, huh? All right, let me right are again. This is, um, are all right. Well, the given activity off the uranium to 35 cent. Bullies given, given activity given activity. Oh, uranium. Um 2 35 2 35 Uh, is our equals 80.0 backroom. The months of the given sample. Most of the given sample M is equal to 1.0 milligram since milli stand to the power minus three. Therefore, a mass is equal to 1.0 Multiply by 10 to the power minus tree, um, 10 to the power minus three, uh, ground 10 to the power minus three grounds. The mother mass of uranium 2 35 Let's say a muller marcie's capital m and the mother muscle feel any, um, to 35 to 35 Crumb, this is the motor Moss Mourner Moss. Oh, uranium 2 35 Mother mass is equal to 35 grounds and the number off, uh, items in the given sample is, uh, and and equals and equals. Uh, massive sample divided by Mother Moss times it will get his number. No, let's ah plugging the values when m is ah one point 1.0 multiply by 10 to the power minus three grounds into it will get his number six points in order to multiply by 10 to the power 23 divided by, uh, mother Moss and Mother Marcie's to 35 grounds and therefore, uh, n equals and is equal to 2.56 multiplied by 10 to the power 18. Adams Adams. Well, no. Let's calculate half life. So half life is equal to 0.6 mine. Three into two point Fight six. Multiply by, uh, 10 to the power 18 Adams divided by divided by 80 back rolls, 80.0 back route. And this gives us, um, half life is equal to 2.2 to multiply by 10 to the power 16 seconds, which is equal to seven point Sydell. Same 1.20 four multiply by 10 to the power eight years so half life equal say 1.0 multiplied by 10 to the power 80 years.

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