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(a) Calculate the energy released in the $\alpha$ decay of $^{238}\mathrm{U}$ (b) What fraction of the mass of a single $^{238} \mathrm{U}$ is destroyed in the decay? The mass of $^{234}\mathrm{Th}$ is 234.043593 $\mathrm{u}$ .(c) Although the fractional mass loss is large for a single nucleus, it is difficult to observe for an entire macroscopic sample of uranium. Why is this?

a) 4.274 $\mathrm{MeV}$b) $1.927 \times 10^{-5}$c) since, the half life of Uranium-238 is very large (4.5 billion years), it decays at a very slow rate.Thus, even fraction of loss mass is large; one cannot observe the loss in mass at macroscopiclevel.

Physics 103

Chapter 31

Radioactivity and Nuclear Physics

Nuclear Physics

Rutgers, The State University of New Jersey

University of Washington

Hope College

Lectures

02:26

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09:41

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02:44

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Let's to part a well, Dr Nucleus off Iranian to 38 after Alfa decays. Tori Um uh 2 34 So, uh, after after decay after daycare. Well, uh, Dr new PS Dr Nucleus. Oh, uranium Uh, two. 30. Eat after Dickie. Um, daughter need yes. Off uranium to 38 is Uh huh. 20. Um do a 34 2 30 four. Well, uh, muscle cranium must off uranium to 38. 38. It's equal to, uh, 2 38 point 2 38 point 0507 Double 80507 Double eight I do it. Don't make mass units on. Similarly, Marcel's podium Uh, 2 34 dude 34. It's equal to, uh 2 34 point 04350 for free. Five, 93 Ah, it don't make mass units and Marsa fell for particle months off. Alpha particle is equal to four point 00 2603 uh 25415 to 5 for 15 It don't make Massey in its You're, uh no. Let's calculate e o Don't m master friends. Well, don't. I am is equal to Marcel's uranium to create uranium to 30. Hit minus. Um, Marcel told him Well, we have Ah, Marcel's, uh, toady. Um uh, 2 34 Um bless, uh, les myself. Uh, alpha particle Marceau fell for particle. Marceau fell for Barnicle. Now let's plug in the values Master Prince is equal to, uh to 38 2 38.50 seven. Double 82 I don't make Massey and it's minus. Uh, then we have ah 2 34 2 34 mind 0.4 359303593 Atomic mass in It's less, uh, four point for 0.26 didn't ring 25415 for 15 atomic mass ins. And simplifying this We have the delta and musical too. Zero point 0045 01045 Uh, mind 19 Mine one line. Don't make Massey annex, and, uh, we know that one. I don't make mass unit eyes equal to 9 21 0.5 1,000,000 electron volts and therefore the energy released They bring the alpha decay. The alpha decay is, uh, e is a cool too on 0.0 for five. 919 It don't make Maxine. It's multiplied by, uh, 9 31.5 1,000,000 electron vote, uh, very atomic mass unit. And this gives us four point four point do seven 74 million electron boat and the fraction off must destroy these Delta am divided by ah, Marce off uranium do 38 and this is dump time is, uh, 0.45 mine. One mine divided by well, most of uranium is to 38 0.50 seven double 87 double eight, uh, two. You don't make mass units and therefore Delta am divided by m, is equal to 1.9 to multiply by 10 to the dollar minus five. Well, uh, the half life of uranium 2 30 It is really high. So half life off uranium to interrogate is equal to four point 468 Multiply by tend to the baller. Nine years Henson up a macroscopic example off geranium. Only few atoms will be became. That's why the changing the masses, not not to civil

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