The halflife of strontium90 is 28 years How long will it tak

The half-life of strontium-90 is 28 years. How long will it take a 76 mg sample to decay to a mass of 19 mg. Answer will be in years.

Solution

half-life of strontium-90 is 28 years

decay constant , k = 0.693/28 =0.02475

N = Noe^(-0.02475t) ;

intial amount No = 76mg ; N = 19mg ; t = ?

19 = 76e^(-0.02475t)

0.25 =e^(-0.02475t)

taking natural log on both sides:

ln(0.25) = -0.02475t

t = 56 years