Problema Solution
Four hundred days after the leak, 9% of the original amount of the substance remained. Determine the half-life of this radioactive isotope.
Answer provided by our tutors
Half life follows the following formula
N(t) = No(1/2)t/to
Where N(t) is the final quantity, No is the original amount, t is the time that has passed, and to is the half life
N(t) = 1 (that's 100%)
No = 0.09 (that's 9%)
t = 400 days
to = ?
1 = 0.09(1/2)400/to
Rearrange to find halflife
to = t*ln(2)/ln(No/N(t))
to = 400*ln(2)/(ln(1/0.09))
to = 400*0.6931/2.4078
to = 115.15
Half life is 115.15 days.