Question 4 [AC 2.4] Explain how the type of decay, the half...

Question 4 [AC 2.4] Explain how the type of decay, the half life and the chemical properties make the following radionuclides suitable for the given applications: a) lodine-131 is used in medicine to monitor the activity of the thyroid gland (\(\beta\) emitter, half life = 8.1 days). b) Americium-241 is commonly used in domestic smoke alarms (\(\alpha\) emitter, half life = 460 years) c) A single gram of polonium will reach a temperature of 500°C making it useful as a source of heat for space equipment (\(\alpha\) emitter, half lives of polonium isotopes range from less than a second to 200 years).

Transcript

00:01 This question is in reference to two radioactive isotopes.

00:06 You are given the rate constants for the two radioactive isotopes, and if you look carefully, you will notice that the rate constants have units of one over a time, one over years in one case and one over days in the other case.

00:21 Because they have units of one over time, they are both first -order processes, all radioactive decays are first -order.

00:31 Processes.

00:33 Because they are first order processes, then we can use the first order half -life equation to solve for the half -life of each of them.

00:44 For amoreseum 241, the half -life equation for first -order processes are is natural log of 2 divided by k, which is provided at 1 .6 times 10 to the negative 3, one over years.

01:01 This then gives this a half -life of 433 years for iodine 125.

01:09 It's the same equation.

01:11 So it'll be t1 .5 equals natural log of 2 divided by its k value 0 .0111 over days.

01:22 So because the k value is now in one over days, then the units for the half -life will be days, and we get 63 days.

01:34 Next, it wants us to, in relative terms, determine which decay occurs faster.

01:42 Well, hopefully it's very obvious to you now with a half -life of 433 years for one of them and 63 days for the other one, that the 63 days, namely iodine 125, is the decay that occurs much more quickly than the amorycium decay.

02:05 So the amoreseum, thank goodness, is going to last many years in your smoke detector.

02:12 For the next part, it wants to know how much of the one milligram sample of each isotope remains after three half -lives.

02:22 Well, if you recall, after three half -lifes, we have cut it in half three times.

02:28 So, after one half -life, we have one -half of the one milligram.

02:33 After two half -lifes, we have one -fourth...

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