Question

(2 points) An unknown radioactive element decays into non-radioactive substances. In 520 days the radioactivity of a sample decreases by 63 percent. (a) What is the half-life of the element? half-life: (days) (b) How long will it take for a sample of 100 mg to decay to 84 mg? time needed: (days)

Answer 1

Answer biven that, In saodays the radioactivity of a Saimple decorases by 63 percent. a bet, No be the initial amount of radioactive subst- cance, and X be a constant, then the amount of Sadio achive element at a time t can be sepaesented af. N(t) = Noekt the amount of radioactive element asted 520 days, alt=520) N(4 - 5%), too – 83 100 No = 0.37 No 4.003706 = No e 520K CONCE) = Noekt In(0.37) --520K HELIN (0.37) 580 R = 10912x10-3. por half life, the amount of radioactive element will be hall of the initial value ie, No12. N(t) = Noekt

Ne = Noekt 1 2 = ekt In(+2) = -kt = -1.912x163€ 1:912X103 t-362.52 ~ 363 days 184 = looe Kt: 0.84 - e-Kt. en (0.84)--Kt.-.-1912x1074 t= ln (0.84) 109/2x10-3 It=91.18 % al days x