My Math Forum The half-life of an element

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 May 27th, 2019, 07:21 PM #1 Senior Member   Joined: Mar 2019 From: TTF area Posts: 136 Thanks: 1 The half-life of an element The half-life of Strontium 90 is about 29 years and it decays into Yttrium 90. Yttrium 90 is also radioactive and is a beta particle emitter with a half-life of 2.67 days. Discuss the amount of Yttrium that would be present in the above example after the Strontium had been decaying for the first 8 days. Firstly I tried to solve this by doing 8/2.67= 2.997 (1/2)^2.997=0.12526 = 12.526% percent of the sample remaining or If you round 2.996254682 to = 3 rounded it = 0.125 decimal or 1/8 as a fraction or 12.5% But was told I'm doing it wrong. Any help is much appreciated, thanks.
 May 28th, 2019, 02:11 AM #2 Global Moderator     Joined: Oct 2008 From: London, Ontario, Canada - The Forest City Posts: 7,963 Thanks: 1148 Math Focus: Elementary mathematics and beyond Are you told how much strontium 90 you are starting out with?
 May 28th, 2019, 04:26 AM #3 Global Moderator   Joined: Dec 2006 Posts: 20,969 Thanks: 2219 One could set up equations that model the general case of arbitrary elements A, B and C, where A decays to B and B decays to C (which is stable), but this seems unnecessarily complicated for the posted problem. For the given question, let's assume that the initial quantity of Strontium 90 is 100kg. As 8 days is very small in comparison with 29 years, it would be acceptable to approximate the rate of production of Yttrium 90 from the Strontium 90 in the first 8 days as 6.59g/day (or a slightly lower daily amount, depending on how it's calculated). This suggests that about 22.2g of Yttrium 90 remain after 8 days. Let's round that amount to 22g (as the figure varies slightly, depending on how you calculate it). So is .022% of the initial mass of Strontium 90 the expected answer? Given that the problem stated "discuss the amount", I suspect that even if you came up with a conclusion such as "very little Yttrium 90 will be present after 8 days", you might still get full credit for your answer. Thanks from helpmeddddd
 May 28th, 2019, 12:09 PM #4 Senior Member   Joined: Mar 2019 From: TTF area Posts: 136 Thanks: 1 @greg. Sadly not.

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