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You can sometimes find deep red crystal vases in antique stores, called uranium glass because their color was produced by doping the glass with uranium. Look up the natural isotopes of uranium and their half-lives, and calculate the activity of such a vase assuming it has 2.00 g of uranium in it. Neglect the activity of any daughter nuclides.

26009 $\mathrm{Bq}$

Physics 103

Chapter 31

Radioactivity and Nuclear Physics

Nuclear Physics

Rutgers, The State University of New Jersey

University of Michigan - Ann Arbor

University of Winnipeg

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Let's write down the givens. Mother must've uranium to 35 is 20 to 35.2 to 4 grams. So, uh, Moeller Maas mourner moss off uranium to 35 to 35. Um, is ah, 23 do Sorry. It's to 35 point zero for crams, and it's ah, percentage abundance is 0.720%. So, uh, person th percent each abundance person get abundance off. Uranium 2 35 Uranium 2 35 is zero point seven 20 or sent and its half life half life half life off. Uranium 2 35 is 7.4 7.4 Multiply by 10 to the power. Um, 80 years and one here equals 3.1 fight multiply returned to the power seven seconds. Uh, one year equals 3.15 multiplied by 10 to the power seven seconds and therefore 7.4 multiply by 10 to the power. Eight years is equal to, um 2.21 Multiply by 10 to the power 16 seconds. And similarly, mother moss, if you're any of do 30 Eighties 2238.25 grams. So Muller Moss Moeller Moss oh, uranium to 38 to a 38 is, uh, 2 38 point, uh, 05 grams, and it's person date abundance. So it's so percentage percent each. Abundance. Abundance, uh, is equal to 99 point 2745% to 7 for fine percent and half life of uranium do 38 half life oh uranium to 38 is 4.47 Multiply by 10 to the power nine years and 4.47 four point for seven multiply by 10 to the power. Nine years is equal to one point for Seattle multiplied by ah, 10 to the power 17 seconds and renal date activity. Let's say activity is a The activity is equal to zero point 693 times and and is the number of items divided by half light, half life. And we know that amount of uranium the combined amount of uranium uranium to 35 when uranium to 30 eighties two grams, so amount of uranium amount. Oh, uranium, uh, combined uranium to 35 when you ran into a tree. It is two grams, two grams and amount of uranium. Ah, to 35 in two grams. So amount ORF uranium 2 35 amount of uranium 2 35 um, in two grams in two grams of food. Then you can be calculated is, uh, uh zero point 7 to 0% off two grands. And this gives us a zero point zero 144 grams. All right? Similarly, um, no. Um, uh. Let us find out the number off Adams in 0.144 grams. So a number of items and equals a 6.0 to multiply by 10 to the power 23 which is will get his number divided by Mother Moss. Eyes do 35 0.4 grams. Multiply by given amount, which is 0.1 for four grams. And this gives us 3.7. Multiply by 10 to the power 19 Adams 19 Adams. All right. So activity of uranium 2 35 Activity off. Uranium 2 35 equals 0.69 Tree multiply body three point seven multiplied by 10 to the power 19. Divided by two point 21 Multiply by 10 to the power 16 seconds, 16 seconds and simply fine. We get ah, 1.16 Multiply by 10 to the power crane. Decay per second on this can be returnees. One 160 Ah, vehicles. So this is the activity of uranium 2 35 Now, let's calculate activity if uranium to 38. So in order to find out the activity of uranium to 38 we need to find out the number off Adam's off uranium to 38 So, um, among toe amount. Oh, uranium 2 38 in two grams off in two grams off uranium Uranium. Well, this can be calculated. Ah, by considering it so ral active abundance. Uh, 99 point 2745 to a 745 percent. Oh, two grams. So among to feeding him to 30 eighties 99.2745% off two grams. And this equals one point 98 549 grounds by for nine grams and number of atoms of fearing him to 38 equals 6.0 to multiply by 10 to the power 23 divided by Moeller moss modern Mosses to 38.5 grams andan multiply by 1.9. Eat five for nine grams and this is equal to, uh, 5.2 Multiply by 10 to the power 21 Adams. So a number of uranium 2 38 atoms is 5.0 to multiply by 10 to 21 Adams. Now, let's find out. Activity little activity off. Uranium 2 38 equals 0.693 Multiply by a number of items. Number of Adams is 5.0 to multiply by 10 to the power uh, 21 divided by half life and half life is one point for zero multiplied by 10 to the power 17 seconds. And this gives us uh, 24,000 uh, 849 back rules 49 back curdled and total activity equals activity. Offer uranium 2 35 less activity off. Iranian to 38 do 38 and this equals, uh 1160 So activity of uranium 2 35 1160 be girls less. Activity of uranium 2 30 eighties 24,000 849 b curls and therefore total activity is equal to total activity is equal to, uh, 26 um, 00 009 Um, backrooms

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