Radium-221 has a half-life of 30 sec. How long will it take for 78% of a sample to decay? (Round your answer to the nearest whole number.)

Answer 1

If 78% decays, that leaves 100-78 = 22% left

half life = 30 seconds

A = Pe^-30r

.5 = e^-30r

take logs

ln(.5) = -30r

r = ln(.5)/-30 = .0231

.22 = e^-t(.0231)

take natural logs of both sides

ln.22 = -.0231t

t = ln.22/-.0231 = 65.5467 seconds to decay 78% of the sample

if the half-life is 30 seconds

75% will decay in 60 days, "1/4 or 25% life"

22% takes a little longer than 25%, so a little more than 60 seconds is required. 65.5446 is a little more than 60 seconds.