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## Homework Statement

The cross section of ##^{59}Co## for capturing the thermal neutrons is ##2000 fm^2##. A ##10g##, thin paper of ##^{59}Co## is radiated for ##100 hours## in reactor with neutron flux ##2\cdot 10^{18} /m^2s##. Density of ##^{59}Co## is ##8.9g/cm^3##. Half life time of ##^{60}Co## is ##5.2 years##.

## Homework Equations

## The Attempt at a Solution

So what happens is ##n+##^{59}Co##->^{60}Co## which than decays with ##t_{1/2}=5.2 years##.

Well, the number of successful collisions is ##dN=\frac{NN_{59}\sigma }{S}## and dividing that by ##dt## gives me ##\frac{dN}{dt}=jN_{59}\sigma ##.

Of course, some of the ##^{60}Co## will immediately start to decay, therefore:

##\frac{dN}{dt}=jN_{59}\sigma -\frac{N}{\tau }##

Solving this differential equations using ##N=C+Ae^{-t/\tau }##

Leaves me with ##N=\tau (jN_{59}\sigma -1)(1-e^{-t\tau })## where ##t/\tau <<1## so

##\frac{N}{t}=jN_{59}\sigma -1= 2.4\cdot 10^{16}Bq## instead of ##6\cdot 10^{11}Bq##.

Note that ##N_{59}=\frac{mN_a}{M}##.

Why is this wrong? :(