Question 545642
The half life of stontium-90 is 28 years.
 How long will it take a 50 mg sample to decay to a mass of 32 mg?
:
Using the half-life formula: A = Ao*2^(-t/h), where
A = resulting amt after t time
Ao = initial amt
t = decay time
h = half-life of substance
:
50*2^(-t/28) = 32
2^(-t/28) = {{{32/50}}}
2^(-t/28) = .64
Using nat logs
ln(2^(-t/28)) = ln(.64)
log equiv of exponents
{{{-t/28}}}*ln(2) = ln(.64)
{{{-t/28}}} = {{{ln(.64)/ln(2)}}}
{{{-t/28}}} = -.643856
t = -.64356) * -28
t ~ +18 years
:
:
Check on your calc: enter 50*2^(-18/28) results: 32.0