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If 1.000 g of 226 Ra produces 0.0001 $\mathrm{mL}$ of the gas 222 $\mathrm{Rn}$ at STP (standard temperature and pressure) in 24 h, what is the half-life of 226 Ra in years?
This is possible only if the half-life is infinite.
Chemistry 102
Chapter 21
Nuclear Chemistry
University of Central Florida
Drexel University
University of Toronto
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okay. To answer this question, let's first recognize that radium can convert into raid on gas through an Alfa decay. So every time one radium undergoes a decomposition a decade event, then it will produce one rate on Adam, the rate at which this is calculated using equation. The decay rate equals the decay constant multiplied by the number of radioactive new Clyde's, which in this case are the radium to 26. Okay, could be calculated using the Half Life, which was given to us as 1599 years. So the decay constant is 4.33 times 10 to the negative 41 over years. According to this equation, if we have one gram of radium, then we can convert grams of radium, two moles of radium molds of radium to number of radium. New Clyde's, which is our end value 2.66 10 to 21 radium New Clyde's. Now we can multiply these two values together in order to figure out how quickly radium is decaying. The initial rate then will be 4.33 10 to the negative four. Sorry is R K value multiplied by the number of radioactive new Clyde's gives us an initial rate of 1.16 times 10 to the 18 decay events occurring per year. But we want to figure out the number of leaders of radium a raid on gas produced and we can get there knowing this decay rate, let me show you. So in one hour period, you can convert two years. We can then use this right here that we just determined to convert years into the number of decay events that occurred and every time of decay. Event occurs every time one of these two K's we produced one Adam of rate on gas. Then we can. Knowing the Adams of Radan gas, we can convert moles of rate on gas by dividing by avocados number. Then, when we know the moles of raid on gas that are produced where it STP And if you remember, there's 22.4 leaders of any gas at STP per mole. So we use this as our final conversion factor in order to calculate the leaders of rate on gas that will be produced by the decomposition of radium in one hour. And it's quite small 4.9 times 10 to the negative nine leaders
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