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Nuclear Chemistry: Nuclear Half Life Calculations

Added Sep 26, 2017 •

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so here's the equation for radium doing alpha decay to make radon and the half-life for this process is 11 days or question is if you start with a 120 gram sample of radium how much will be left after 44 days the first thing that's do is figure out how many half-lives 44 days is going to be okay so what Half-Life is 11 days so 44 days is going to be for half-life's okay nothing else going to be for Half Lives let's just make out a will chart and figure out how much we're going to have it each step so starting with 420 G after one half-life will have half of that so have 60 grams okay that's the first half life now second half life will go from 60 down to 32 Half Lives will go to 15 gram and now our fourth Half-Life will give us 7.5 grams so 7.5 g is how much rating will have left after 44 days or a four half-lives now a lot of times when people ask questions about half lives they want to know about percent and fractions to soap let's see how we dancer if we were asked what percentage will be left after 44 days okay instead of what amount this is this is really simple it's actually easier than this case over for the percent left will do the same thing just assume that we start at a hundred percent okay so hundred percent is where we start after one half-life how much would we left well half of it which is 50% so there's our first now our second half life will go from V percent down to 25% our third half life will go to 12.5% okay and then for our fourth half life will go to 6.25% and this is what percentage of the starting amount of have left after 44 days or 4 half-lives finally if you are asked to find the fraction that was left after 44 days how you doing keep in mind again this weekend before half life so after one half life we have one half left okay now we multiply that after two half-lives another half so now we have 1/2 x 1/2 1/4 left after two half-lives we're going to lose another half so now to happen to have time to half we have one eighth left and finally a fourth half we're going to have 1/16 of the original amount left and if you do 1/16 and turn that into a percent it's 6.25 that's how you can solve a problem like this for the ACT come out the percent and for the fractional amount here's our next question hydrogen 3 which is also known as tritium undergoes beta Decay to make helium-3 and this process has a half life of 12 points three years so sample tritium decays leaving 2.5 grams of tritium how long will this take okay let's figure it out by just making a chart like we did before so we're starting with 80 grams of tritium one half life is going to give us how much 40 grams okay one half life now we're going to do another half life now it's down to 22 1/2 down one more 10 grams another one 5G and finally down to 2.5 grams so that is one two three four five Half Lives cast of five Half Lives how much does each half life take each half life takes 12.5 years so I can do 12:00 5 * 12.3 year so we can do 12.3 times 5 is going to give us 61.5 years that's how long this whole process would take okay what if the question involved percentages asking how much are how long it would take if we were left with 3.1% I'm going to do this really fast so that you can do it on your own Open start with 100% take that down 50% and then another half life would give us 25% 12.5% 6.25% and finally 3.125% that's pretty close to 3.1 they're talking about it's the same as it's 1 2 3 4 5 Half Lives 61.5 years. Finally what would happen if you were given come out as a fraction asking how long will it take to get down to 1/32 of the original amount which is multiply 1/2 together and see how many will need to do 1/2 x 1/2 that's 1/4 1/16 1/32 each one of these one half's represent one half life so that's how we could get five half lives with fractions 5 T 1/2 okay let's do one more equation for thallium undergoing beta Decay to make lead but we don't know the half life you're going to have to figure out what it is so the question asks if we start with 200 g of fat 207 here after 20 minutes there's only 12.5 mg of Valium left what is a half-life in the Decay process as usual let's make a chart that shows how much this is the king so we start with 200 grams one half life is going to knock us down to 100 grams now another half life will take us down to 50 g then we'll get down to 25 grams and finally a fourth half life will take it down to 12.5 grams so we have one two three four Half Lives or half lives no it said that this whole that's to go from $200 down to 12.5 gram takes 20 minutes in that 20 minutes there have been four half lives so to figure out the length of one half life we're just going to do 20 that time / for Half Lives which is going to give us 5 minutes for the length of one half life and as I've shown you in the previous examples you could also do this with percent by starting at 100% and working your way down or if the number had to do with fractions just multiply 1/2 together for each half life that you have not the calculations we've done for all these problems so far I do them in your head pretty well you just take numbers and cut them in half a bunch of times and do some relatively simple math but there are a bunch of half life problems that require trickier math that use exponents and logarithms I will now talk about those in the neck

Uploaded by Laura Houston.

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Nuclear Chemistry: Nuclear Half Life Calculations

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