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Irradiating ourselves! The radiocarbon in our bodies is one of the naturally occurring sources of radiation. Let's see how large a dose we receive. "C decays via $\beta^{-}$ emission, and 18$\%$ of our body's mass is carbon. (a) Write out the decay scheme of carbon-14 and show the end product. (A neutrino is also produced.) (b) Neglecting the effects of the neutrino, how much kinetic energy (in MeV) is released per decay? The atomic mass of $\mathrm{C}-14$ is 14.003242 $\mathrm{u}$ (See Table $30.2 . )$ (c) How many grams of carbon are there in a 75 $\mathrm{kg}$ person? How many decays per second does this carbon produce? (d) Assuming that all the energy released in these decays is absorbed by the body, how many MeV/s and J/s does the $\mathrm{C}-14$ release in this person's body? (e) Consult Table 30.3 and use the largest appropriate $\mathrm{RBE}$ for the particles involved. What radiation dose does the person give himself in a year, in Gy, rad, Sv, and rem?

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a. $\stackrel{14}{7} \mathrm{N}($ Nitrogen $)$b. 0.156492 $\mathrm{MeV}$c. 3452 decays/sd. $864 \times 10^{-13} \mathrm{J} / \mathrm{s}$e. 3.64 rem/year

Physics 103

Chapter 30

Nuclear and High-Energy Physics

Atomic Physics

Nuclear Physics

Particle Physics

Cornell University

University of Washington

Hope College

McMaster University

Lectures

02:42

Atomic physics is the field of physics that studies atoms as an isolated system of electrons and an atomic nucleus. It is primarily concerned with the arrangement of electrons around the nucleus and the processes by which these arrangements change. The theory of quantum mechanics, a set of mathematical rules that describe the behaviour of matter and its interactions, provides a good model for the description of atomic structure and properties.

02:26

In physics, nuclear physics is the field of physics that studies the constituents and interactions of atomic nuclei. The most commonly known applications of nuclear physics are nuclear power generation and nuclear weapons technology, but the research has provided application in many fields, including those in nuclear medicine and magnetic resonance imaging, ion implantation in materials engineering, and radiocarbon dating in geology and archaeology.

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Problem 10.(Carbon-14 …

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billings is question We need to check holds a carpenter, the only body details and part when they ask us to write out. So deface came off Cover 40 and shows an product. And you, Trina, was awesome, pretties. And so question, which tells us that it's a bit of minus decay. So Covering 14 has the for Miller off C 16 for so well, firstly, no better decay. Sai Electron is produced is in question tells us that a neutrino is also produced in a better decay. What happens is that its atomic number becomes increases their work because in a better decay, a neutral becomes a proton, and a natural incense at an actual is emitted outside of the other. So when we look at this will see that inability, case and mass off thing does not does not change its still 14 because when's the neutron change form and you turned your proton. It's mess usual. Problem has, frankly, it's a mess with mess doesn't change presents. Atomic number increased by one. So it goes from 6 to 7, and what element has atomic number of seven? It is nitrogen. So in now we double check is mass conserved his masses. Replicant, sir, because thes to have roughly zero mass or technical magical mess is electric charge conserved? Um, let's see. Previously it has no electric church afterwards. It actually says is actually Ira. It is not. It is not an Adama Siro, because when you think about it, it's a neutral in the current D case into an actual end. A protons. The election gets admitted, but the proton remains inside. So Adam and actually introduces one positive charge. So that is scheme. We have also in calculation. We already kind of We don't care about this process because it doesn't matter. It doesn't affect the mess. Um, okay, so that's part a Mr Perfect Art pieces how much kinetic energy is released in this decay. So I guess we first need to find mass decreases. Reclines mess of carbon 14 sub track mass of actual subtract. It's a mass of nitrogen, so use new cure masses. Um, so is the reason we use nuclear masses to make sure we do not need to come first. Atomic collections to simplify the process. So the nuclear mass, um, for covered 14 is Cover 14 has 14 ministers you are three t o for to you, Burt. We need to subtract six legs obsessed times. Massive doctrine. So it is 13.999950 What about nutrition from nitrogen? It's 14.307 for you. Subtract six Empty, which is 13.999234 Hugh. Okay, And finally, let's look. It's d o m m iss 13 point ni ni ni ni from Siri Some count. 13.999 234 You subtract said Mass of the election. It is 1.67 times tend to nectar for you. So this is a no b Use the energy Cronus Times. This's energy corresponding to every you are. I was going This's country by e equals m. C. Squared. And we've found this in section one. This gives us energy equivalent of 0.156 MTV. Only part see asks on a calm day. Grants of Carbon is hearing a 65 kilogram person in Normandy. Hits per second doesn't produce, so we know 18% off a person is Carlos So zero queens, so their point intern hands 75 killed Gran is 13.5 kilograms. That's someone of currently in person and already from example 30 point for We know that so pretty much in this book, if you do not have certain numbers, you're afraid who takes from the example it six empowered to give his constants. So here example 30 point, for we know that activity to to, well, gram of carbon is 0.255 Think so. Is it because of that? What we have to do, too? 13.5 children off Coven is 13.5 times 10 to these third grand times we have 0.255 back. Prue Graham since gives us 3.4 times 10 to assert are back. But Buck is equivalent to your d case per second. So because of that, we nose at Sidi K's per second. Our in our body in a 75 1 person is certainly so. Print five times 10 to the 30 case and party. Let's see, are running out of space little bit and move everything into that Some change to select everything moved on to his left so that I have a little more space great. Okay, so let's continue for party assuming or energy released. This defense is absorbed by the body at home. Much evey orjust president is such so each of decay releases Sirrah 0.156 maybe and then airstrip in four times into the 30 case per second. So we times, um, we have times 10 to the third deep. His press second times 0.156 m p b Crip, decayed and sad is a total of 5 30 maybe Chris seven. And if we convert that ajar, it's 8.5 times 10 tizzy inactive. 11 jaws per second party. Um, it's very question console Table 30 Part three and use our largest approximate Artie Evil of particle. You've oft what radiation as a person give himself in a year. So it's in the R B is tell us what our best platoons of is largest appropriate. R B. What do we have? 30.3? To be honest, I think maybe we should just use our be off electric, which is one because I think it doesn't seem to. It's not offer decay. It's not, and it doesn't sake what Decatur's so if it's beta decay because we produce a lecture. I am going to use our B off election, which is one. So let's say, um so total energy absorbed in a year is 8.5 times. Tent is negative. Learn just for second terms. In a year, we heard 3.146 times 10 to the cylinder seconds, and so there are in a year were absorbed into 17 times 10 to the negative. Three. Char and sells. Absorbed dose is absorbed. Houses usually settle her image. Absorb. Divided by a za mass, the size and collective suitor are divided by 35 Kilger, which was 3.6 times turn to see nectar, five tours per kilogram. So this is also equal to, um, just print program. So thiss is equal to certainly soup. When six times 10 to the negative five gray, which is equal to sleep on six times 10 tizzy. Negative three rat. So it's 3.6. Um, merely rat. And then because for elections we have R B equals one. So soup went 6,000,000. Rod is Chris. Take responds to 3.6 and red. Okay. Um, so this is ISS Ramsay's system. Brad, you also question also asked us to express it in Korea's is easily counsel. Every castle whose ass is this is 36. You, uh, chief, why me? Agree? And CeCe is 36 meal as he sees it as a unit about so that's the answer to off five sections of this question.

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