Question

(b) [5 marks] Using first principles, derive the radioactive decay rate for nuclei whose decay constant is ?. Here R,-??, is the rate of decay at t-0 [5 marks] A count-rate meter is used to measure the activity of a given sample. At one instance it shows 4750 counts per minute (cpm). Five minutes later it shows 2700 cpm. Find the decay constant and the half-life of the sample. (c) (d) [5 Marks] For alpha decay, show that 13 markel Thus for 212 Ri ?208 TI He+O calculate K

Answer 1

(b) Let initially R_o be the number of radio active element, after time t present Under cay element is R Therefore Roc. Let R be the present of a radioactive element and time dt , number of decay element of R. Therefore dR - alpha - dt R [Because lambda = decay constant] integral d R/R = -lambda integral dt [Because negative sign for decreasing of dN with increasing dt. ln R = -lambda t + log A [log A = integration constant] R = Ae^- lambda t initial condition at t = 0, R = R_0 Therefore R_0 = A Therefore R = R_0 e^- lambda t \r\n (e) R = R_0 e^- lambda t R_1 = 4750 t_1 = 60 sec R_2 = 2700 t_2 = 5 times 60 sec = 300 see Therefore 4750 = R e^-60 lambda (1) 2700 = R_0 e^-300 lambda (2) Therefore 475