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Problem 65 Hard Difficulty

SSM The nuclide 198 Au, with a half-life of $2.70 \mathrm{d},$ is used in cancer therapy. What mass of this nuclide is required to produce
an activity of 250 $\mathrm{Ci}$ ?

Answer

$1.02 \mathrm{mg}$

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Video Transcript

Mass. We first right Curie in the back rules. We know one curie, one curie is equal Thio creep or in seven times, 10 to the power 10 back rolls back rolls. And this is equal to 3.7 times 10 to the power dent Disintegration CZ for a second. The decay rate are are is related to the number off nuclear I am by relation that is our physical to lend a times. And where Linda, is this integration constant? The disintegration constant we know is related to the half life by Eleanor for two divided by half life. And from here we can express end so and will be equal to our divided by lambda, which is a call to Artie Half Life or L A ball for two once we found. And then we can easily find the mask Bye Went flying with in Nord So moss will be 10 times. Ah Lord, let's first find it. And so we confined end by substituting your values here. So, um all right, Isa to 50 Curie. So Curie want to apply my 3.7 times 10 to the power Then we could work this into back rolls SA unit times half life, which is a 2.52 point seven days. And then we multiply 2.7 to 0.7 days. With this seconds in the day, they 0.64 times 10 to the power four seconds in a day to convert this into an S I unit divided by Ellen off the two. Then we get the number number off nuclear to be 3.11 times 10 to the power 18 From here, we know the muscle for you. You won 98. Hmm. And more is equal to 1 98 atomic mass units times 1.661 times 10 to the power minus 24 grams. We have in one atomic mass units excuse us 3.29 times 10 to the power minus 22 grams. Then we can simply meant apply the end with them not to find the mask, so m will be cool. Thio 3.11 times 10 to the power 18 that we got earlier times 3.29 times 10 to the power minus 22 grams. Ah, so when you find these two numbers we get 1.2 times 10 to the power minus three grams, which is called the one for 02 milligrams.