A sample contains 950104 radioactive nuclei In a time of 3 m

A sample contains 9.50×104 radioactive nuclei. In a time of 3 minutes, 2.70x103 of the nuclei decay Evaluate the half life of the sample (in minutes) Use the equation for the radioactive decay law Submit AnswerIncorrect. Tries 1/10 Previous Tries

Solution

N(t) = N(1/2)^(t/th)

where, N is initial amount

N(t) is the amount remaining after time t

th is the half life time, ie, time for half the amount to decay

Amount remaining after 3 min is 95000 – 2700 = 92300

92300 = 95000(1/2)^(3/th)

(1/2)^(3/th) = 0.97

log [ (1/2)^(3/th) ] = log 0.97 = –0.013

3/th log (1/2) = –0.013

3/th (–0.30) = –0.013

3/th = 0.043

th = 3/0.043 = 69.77 minutes