Respuesta :
[tex]4.9[/tex]⨯[tex]10^{-9}[/tex] volume of radon will be produced per hour at STP from 1.000 g of ²²⁶Ra (t₁/₂ = 1599 yr; 1 yr = 8766 h; mass of one ²²⁶Ra atom = 226.025402 amu)
Briefly explained
Let's first recognize that radium can convert into radon gas through an Alpha decay. So every time one radium undergoes a decomposition a decay event, then it will produce one rate on atom , 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. 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 atoms of rate on gas. Then we can. Knowing the atoms of Radon gas, we can convert moles of rate on gas by dividing by avocados number.
Then, when we know the moles of radon 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 [tex]4.9[/tex]⨯[tex]10^{-9}[/tex]
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