SOLUTION: A research assistant made 160 mg of radioactive sodium (Na^24) and found that there was only 20 mg left 45 h later. (a) What is the half-life of Na^24? (b) If the laboratory

Algebra ->  Exponential-and-logarithmic-functions -> SOLUTION: A research assistant made 160 mg of radioactive sodium (Na^24) and found that there was only 20 mg left 45 h later. (a) What is the half-life of Na^24? (b) If the laboratory       Log On


   

Question 936000: A research assistant made 160 mg of radioactive sodium (Na^24) and found that there was only 20 mg left 45 h later.
(a) What is the half-life of Na^24?
(b) If the laboratory requires 100 mg of Na^24 12 hours from now, how much Na^24 should the research assistant make now? (Ignore the 20mg she currently has)
Answer by josgarithmetic(39618) About Me  (Show Source):
You can put this solution on YOUR website!
General model is N=N%5Bo%5De%5E%28-kt%29


ln%28N%29=ln%28N%5Bo%5D%29-kt
ln%28N%29-ln%28N%5Bo%5D%29=-kt
kt=ln%28N%5Bo%5D%29-ln%28N%29
k=%281%2Ft%29ln%28N%5Bo%5D%2Fln%28N%29%29------use this to find the value for k.

k=%281%2F45%29%28ln%28160%2F20%29%29
k=%281%2F45%29ln%288%29
highlight%28k=0.046%29

You can return to this one, kt=ln%28N%5Bo%5D%29-ln%28N%29 , to determine the half-life.
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t=%281%2Fk%29ln%28N%5Bo%5D%2FN%29
t=%281%2Fk%29ln%282%29
t=%281%2F0.046%29ln%282%29
highlight%28t%5Bhalf%5D=15.07%29, maybe more accuracy than reasonable.

Your more specific decay model is N=N%5Bo%5De%5E%28-0.046t%29.
Now you have a known N but you want to solve for N%5Bo%5D.