A sample of a radioisotope contains 10,000 grams and has a half of 2 days. How many days pass before only 625 grams of the isotope remain?

Question

jfraser · Answer

every time one half-life passes, half of the sample has decayed. How many times can you "cut" 10,000 in half until you're left with 625? Each "cut" is the passing of one half-life

anonymous · Answer

Is that the answer? I still don't understand

danjs · Answer

Amount Remaining = Original Amount x (1/2)^(#half lives)$$625 = 10000*[\frac{ 1 }{ 2 }]^t$$

solve for t, the number of half lives. then multiply that by 2 years per half life.

danjs · Answer

2 days per half life, sorry

danjs · Answer

or simply do what JF said above, and keep dividing 10000 by 2 until you get to 625 and count how many times it takes to get there. then multiply that by 2 days. 
Only works easily if it is a nice problem from the book, where you get a whole number of half lives.

jfraser · Answer

half-life problems always start out with the nice, easy approach of cutting everything in half multiple times, THEN they pull out the more complicated math. The simplest explanation is usually the best, until they get really familiar with the process