Question

Please answer question and show all work! Provide any justification. Here is a link to the book. This is from chapter 2!! https://www.math.wustl.edu/~sk/books/newhist.pdf

A certain radioactive material has the property that half the substance present decays every three hours. If there are 10 grams present at 10:00am on Monday, then how much material will remain at 10:00am on Thursday of that same week? [Hint: You cannot solve this problem lessons of this chapter.]

Answer 1

eq^n of radio achive decay: - N(t) = N_0 e^- lambda t t = 1/tau, tau = T_HL/ln2 T_HK = 3hr (half life) Rightarrow N(t) = N_0 e^- ln 2 t/3 t is in hrs N_0 - no of particle present on Monday 10: 00 am. initial mass M_0 = A_r N_0/L A_r - atomic no L rightarrow avagadno's constant for mass on Thursday 10: 00 Am left calculate no.of particles present on Thursday 10: 00 am mon - tue - wed - thurs 3 times 24 = 72 hrs = t N_T = N(72) = N_0 e^- ln 2/72/3 = N_0 e^ln(2)^- 24 N_T/N_0 = e^ln2^- 24 = 2^- 24 N_T A_r/L = M_T - mass present on Thursday Rightarrow N_T/N_0 = M_T/M_0 = 2^- 24 M_0 = 10 grms (given) M_T = 10 times 2^- 24 gms will be present on thrusday 10: 00 am.