Question

27. Radioactive decay is modeled by this function where R is the ratio of remaining material and k is the rate of decay. (t is time in years) R=en a. Wh When 800 years have passed, the material has lost 20% of its radioactivity, so R is 0.80 (i.e. 80% is left). Find the rate of decay. b. Use the exact rate of decay from part a. Find the half-life of this element. (Half-life means only 50% of radioactivity is left, so R=0.5)

Answer 1

It is given that - function of radioae fue decay - R=ekt (i) Where Rn dahoo Remaining material CE . Kui dece rate of decay - t u time in years. (2) When t = 800 years - R=0.00 (one Put the valen of Randt inegócia (? 4 = 80 =0.0 Ct=100-20 0.Da ok* 806 I Go *100=0.0 happy (0.) = eBook log (0.8)=8ook log (0.8) 800 -0.22314 K at 0.0002 0 800 00 i rake cy dleccy - 50.00028)

(b) when R=0.5 kt -0.00028 € and ke-0.00028 Aut the value of Randk in egni Raee 0.5=e loy (0-5)= -0.000287 to log (0.5) (-0.00028) 60.69314) - 0100028) " half life for this sadioactive element = 24755 years x 247505 years