Question

If the half-life of a given substance is 100 days, how long will it take for a 50 gram sample of the substance to decay until there is only 6.25 grams of the radioactive material remaining?

Answer 1

50 grams decay to 25 gram in 100 days and divide by 2 again and again one more till you get 6.25 and count how many times have you divided by 2 multiply it by each half life 100 days so the time to decay is 300 days

Answer 2

The formula for exponential decay is:
\[m=m _{0}(\frac{1}{2})^{\frac{ t }{ t _{1/2} }}\]
"m" is final mass
"m(0)" is starting mass
"t" is total time passed
"t(½)" is length of half-life

If you take the total time passed and divide by the half-life, you get the NUMBER of half lives (that's what the exponent in the equation gives you). For every half-life that passes, your starting mass is halved.

We're given most of this information in the question, so just sub in the numbers and solve for the unknown!

\[6.25=50(\frac{ 1 }{ 2 })^{\frac{ t }{ 100 }}\]