if a radioactive element has a 5.23 days half-life and a beginning mass of 500g and has 3.90625g left. how old is the material and how many half-lives did it undergo?

DarkCalculis
Feb 22, 2018

#1**+3 **

OK, DC...we have this

3.90625 = 500 (1/2) ^(t/5.23) where t is in days

Divide both sides by 500

3.90625 / 500 = (1/2)^(t/5.23) take the log of both sides

log ( 3.90625 / 500) = log (1/2)^(t/5.23) and we can write

log (3.90625 / 500) = (t / 5.23) * log (1/2)

Multiply both sides by 5.23 / log (1/2)

log (3.90625 / 500) * (5.23 / log (1/2) ) = t ≈ 36.61 days

To find the number of half-lives we have

36.61 / 5.23 = 7 half-lives

CPhill
Feb 22, 2018

#4**+3 **

Another take (but similar)

500 e^-kt = 250 to solve for k we will let t= number of half lives= 1 (as in ONE half life)

k = ln (250/500) / -1 k=.693147

Now for the sample

500 e^-.693147 t = 3.90625

t = #half lifes = ln (3.90625/5000) / - .693147 t = 7.00 half lifes (or is it half LIVES ?)

ElectricPavlov
Feb 22, 2018