Calculating Co-60 Produced from Co-50 in 1 Week

[ineedhlp]

Co-60 is produced from Co-50 through neutron activation. Neutron flux 10^18 nuetrons/(s*m^2). cross section is 20 barns and the mass of Co-50 40mg. How many Co-60 are produced in one week?

My attempt:
I multiplied the flux by the seconds in one week and by 20 barns in m^2 and got 0.0122 neutrons. Then found how many atoms are in the 40mg of CO-50 which was 4.08598x10^20 atoms. Then i multiplied the amount of atoms by the number of neutrons in Co-59 and add to the number of neutrons found by the flux and then divided by 33 neutrons for how many are in C0-60. This gave me the number of nuclei of Co-60 found which was not the right answer.

 

[mfb]

I think C-50 should be C-59 everywhere.

I multiplied the flux by the seconds in one week and by 20 barns in m^2 and got 0.0122 neutrons.

Careful, the unit is more like "neutrons per atom".

Then i multiplied the amount of atoms by the number of neutrons in Co-59

Why?
The reaction involves the whole nucleus, and the cross-section is "per nucleus".

and then divided by 33 neutrons for how many are in C0-60.

Again, why?

 

[ineedhlp]

I assumed that if i had the total number of neutrons of the CO-59 and added it to the number of neutrons that came from the flux, i could find the total number of Co-60 neutrons and then find how many nuclei from that.

 

[mfb]

You don't have the total number of neutrons in the beam, and you don't need it.