Question

Alpha particles of kinetic energy 6.8 MeV are incident at a rate of 2.9 x 107 per second on an aluminum foil of thickness 2.9 x 10-6 m. A circular detector of diameter 1.0 cm is placed 14 cm from the foil at an angle of 30° with the direction of the incident alpha particles. At what rate does the detector measure scattered alpha particles? (The molar mass of aluminum is 27.0 g/mol and its density is 2.7 g/cm3.) s-1

Answer 1

Expression for Rutherfond scattering enom-section in 29 L x2 N(O) = nt [ Tue las T Rk ul un& sin (%) Relation between number of moles (n), avogacho number (NA) ondecolar weight (M) and density (8) is n= WAS = 60023 x 13 x 267x106 M 27

28 6,023 x 10 ne 0.6023 x 10 e UT & = 1044 mer fm N8) 22 -6 Grb 023X10X2:9519 nicol) = 6.525x180 x 20 xi ( 21941-19 Jordan 28 6.023 X 10 X 2.9 X10 2x13*1.44 N(O)= 4X (0.147² 2x 6.8 mev J N (8) = 0.003763 on 2 2 aree of the detector n. A = T (ousemo z 7.8 x 10 m2 to total probability of x- particle to strike the detector in Nosotal = 7, 854 x 105 x 0. 0037 63 = 2.96* 107 Here, rate of incident particle is 200 x 10 pensec so nate at which they strike the oletection is (2.96% 13 %) x (2.9 xp?) = 8.584 peanec, 7