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Radioactive isotopes used in cancer therapy have a "shelf- life," like pharmaceuticals used in chemotherapy. Just after it has been manufactured in a nuclear reactor, the activity of a sample of $^{60} \mathrm{Co}$ is 5000 Ci. When its activity falls below 3500 Ci, it is considered too weak a source to use in treatment. You work in the radiology department of a large hospital. One of these $^{60} \mathrm{Co}$ sources in your inventory was manufactured on October $6,2008 .$ It is now April $6,2011 .$ Is the source still usable? The half-life of $^{60} \mathrm{Co}$ is 5.271 years.

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3600 $\mathrm{Ci}$

Physics 103

Chapter 30

Nuclear and High-Energy Physics

Atomic Physics

Nuclear Physics

Particle Physics

Rutgers, The State University of New Jersey

University of Washington

Simon Fraser University

Hope College

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.

02:05

Radioactive isotopes used …

03:49

01:01

01:22

01:52

43.22. Radioactive isotope…

02:53

A 5000-Ci 60Co source used…

03:21

An unstable isotope of cob…

Cobalt-60 $\left({ }^{60} …

02:11

Cobalt- $60\left({ }^{60} …

02:35

A device used in radiation…

01:42

Cancer cells are more vuln…

is this question. You're working in a can so therapy hospital and then you have her radioactive source in this source. It has the initial decay rate off 5000 Curie. So in this case, let's did not Ah, the activity of the simple ISS a sook is the rate of decay. Um, in thiss according to the equation is Linda comes in Something's a previous chapters. We already improving questions. We already knows that the simple around n the case exponentially so because they is proportional to end, we know a also t case exponentially. So we have a question and equals a not times e lend selective ability. So they know what we already know is the initial rate is 5000 Curi. And this question asks if the simple wass are manufactured October 662 thousand eight, and now it's October 8 April 6 2011. Is the source still usable? So that is asking us to calculate a certain time in a such a Linda and Linda is something to find because we know the half of silicon, right? Linda, and time is from two thousand 2 8 to 2, some 11 at this time period is a current, eh? Still larger? Said 3500 Curie. So this trip is his store's Still usable. Is is a radioactive if is a radio action still strong enough for it to be used as a source? So let's first try to find what the decay constant Lambda is. So we have Clinton equals flowing to over the half life End's 1/2 life is 5.271 years. So it's 0.1315 here, so usually weak, we convert see sinks into seconds. And here I'm not doing seconds because is disgusting. I'm using years as a unit from beginning to end. So I s long as I keep everything consistent. It is fine. So now let's go back and calculate a T. The knot is five Southern Curie times E to the negative. So no 0.131 The river's times, um so time cure from two thousand 2 8 October 2 2011 April. It's about it's a lot to years in 1/2 so it's 2.5 years. Excuse us 3600. See I So it's the slaughters and 3500? Yes, it is above the minute it is a bustling. Nobody's is very close. So sis sources barely usable

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