SOLUTION: Complete the table for the radioactive isotope. (Round your answer to two decimal places.) isotope: RA^226 Half Life (Years): 1599 Initial Quantity: 10g Amount after 1000 ye

Question 1118991: Complete the table for the radioactive isotope. (Round your answer to two decimal places.)
isotope: RA^226
Half Life (Years): 1599
Initial Quantity: 10g
Amount after 1000 years: UNKNOWN
Found 3 solutions by josgarithmetic, ikleyn, greenestamps:
Answer by josgarithmetic(39618)   (Show Source): You can put this solution on YOUR website!

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Answer by ikleyn(52788)   (Show Source): You can put this solution on YOUR website!
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The fact that half-life is 1599 years means that M(t) = M*2^(-t/1599)), (1) where M is the initial mass of the isotope, M(t) is its current mass at the current time moment t. Indeed, at t = 1599 years you have from the formula (1) M(1599) = . Then at t = 1000 years the remaining mass of the initial 10 grams is M(1000) = 10*2^(-1000/1599) = = 10*0.6482 = 6.482 grams. Answer. 6.482 grams of the isotope after 1000 years.

Answer by greenestamps(13200)   (Show Source): You can put this solution on YOUR website!

The solution by tutor @josgarithmetic, using logs, ends up with the right answer but seems like a very inefficient way to solve the problem.

The solution by tutor @ikleyn is much simpler and also obtains the right answer. But I note that scientists like to use exponentials with negative exponents to indicate decay, so her initial equation is

where n is the number of half lives.

For me, it is much more natural to write the equation in a way that clearly shows the amount remaining becomes half as much after each half life:

So my path to the solution of the problem would be a single calculation:

Use both methods as you practice other half life problems and see which works better for you.
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