2.66666666666667 grams
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59.25 secondsAfter 1 half-life: 16*(1/2) = 8 g remainsAfter 2 half-lives: 8*(1/2) = 4g remainsAfter 3 half-lvies: 4*(1/2) = 2g remainsAfter 4 half-lives: 2*(1/2) = 1g remainsSo after 4 half-lves you have 1 gram of Na25 left. This is also the amount remaining after 237 seconds. Since 4 half-lives have elapsed over 237 seconds, you can divide 237 seconds by 4 to find the half-life of Na25 is 59.25 seconds.You can also figure it out using the rate of decay formula:At = Ao*e-ktwhere Ao is the initial amount, At is the amount left after some time t. k is the decay constant which is k = ln 2 / t1/2 where t1/2 is the half-life.In this case Ao = 16g, At = 1g, t=237 secSubstitute in the formula to solve for k, then take the answer for k and use it in the other formula to solve for the half-life (t1/2):1 = 16*e-237kln (1/16) = ln (e-237k)-2.7726 = -237kk = -2.7726/-237 = 0.011699 sec-1t1/2 = ln 2/k = 0.693147/0.011699 sec-1t1/2 = 59.25 sec
1/8 amount of the element will reamain. After 1 half-life there is 1/2 left After the 2nd half-life there is 1/2 of 1/2 left which is 1/4 After the 3rd half-life there is 1/2 of 1/4 left which is 1/8
It is a half left side triangle, nothing more, nothing less.
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