Question

Calculate the activity in mCi and MBq of In-113 produced by irradiation of 1 g of pure Cd-111 for 3 hr with 12 MeV protons having a beam intensity of 1x10¹³ particles/(cm²-sec). The cross section for formation of In-111 (T = 2.8 d) is 200 millibarns ( 1 mb = 1x10^-27 cm²). Recall 1 mCi = 37 MBq

Answer 1

Number of In-111 produced in 3 Hr is given by:

where, n is particles incedent per second per unit area, n = 1 x 10¹³ /cm²s

n_s is number of source particles , ie. (1/111)x 6.022 x 10²³ = 5.425 x 10²¹

sigma is crossection of formation = 200 x 10^-3 x 10^-24 cm² (given incorrect in statement)

t is time of irradiation. t = 3 x 60 x 60 s = 10800 s

hence, number of In-2.8 atoms:

Half life of In-111 T_1/2 = 2.8 days = 2.8 x 24 x 60 x 60 s

T_1/2 = 241920 s

As radioactivity constant is given by:

/s

As initial activity is

Hence, we can write as:

and

as required