Polonium-209, an a emitter, has a half-life of 102 years. How many alpha particles are emitted in 1.0 s from a 1.0 ng sample of 209Po?

Video transcript

Hello everyone today we have the following problem radon 222 has a half life of 3.82 days. And emits alpha particles, calculate the number of alpha particles released from a one microgram sample of radon 222 in one minute. So first we have to transform Or convert the days in two minutes from our half life. So we're gonna start off with our 3.82 days We're gonna use the conversion factor that for every one day we have 24 hours And furthermore we can see that in one hour we have 60 minutes. And so when our units ultimately canceled out we're gonna be left with 5500 0.8 minutes. So this is our half life represented in minutes. Next we're gonna try and use those minutes to find our constant or constant K. And that can be represented by the natural log of two divided by our halftime We have our natural log of 2.5 time in minutes we calculated was 5,000.8 minutes. This is gonna give us 1.26 times 10 to the negative fourth minutes to negative one next we could calculate the number of Raid on 222 Adams represented by in we're going to take our one microgram sample of our Radan. We're gonna convert this into grams by using the conversion factor that one microgram is equal to 10 to the negative six g. And then we're going to multiply by our molar mass of radon which is one mole of Reagan equaling 222 grams of Reagan. And this is found by the periodic table and also in the question stem. And then lastly because we want alpha particles or atoms, we're going to use the conversion factor that in one mole of this raid on we have and this is going to be avocados number 6.02 times 10 to the 23rd atoms. Once our units cancel out, We're gonna be left with 2.7, 1 times 10 to the 15th atoms. So we have the number here. However, we need to lastly calculate the rate and this is going to tell us how many particles are released in a given minute for our sample. And the rate is going to be calculated from our value of K times our value of n. Our value of K. What we calculated earlier was 1.26 times 10 to the negative fourth minutes. The negative one times the number of rate on atoms that we just calculated as well, which was 2.71 times 10 to the 15th atoms. And this calculation is going to give us 3.418 times 10 to the 11th Adams per minute. And so this is going to translate to 3.42 alpha particles That are released in our sample in one minute. And so with that we've answered the question overall. I hope this helped. And until next time.