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How many beta particles are emitted in 43.3 s by a 2.98-mg sample of 60Co

Submitted by Anonymous (not verified) on Wed, 04/08/2009 - 22:56

Hey all, I've ran into a bit of a mess with this problem:

Cobalt-60, which undergoes beta decay, has a half-life of 5.26 yr.

(a) How many beta particles are emitted in 43.3 s by a 2.98-mg sample of 60Co?

(b) What is the activity of the sample in Bq?

Alright, here is what I've done so far to try to get a solution.

First off, I figured since you are given the half-life, you can easily find k and this got me 0.132 yr^-1.

After this I became confused as to what you do with the k value. I know once the correct Nt is found, it is multiplied by 1/60 and then Avagadro's number in order to get the particle number, but I don't know how to get the correct Nt value.

Further on, I know once you get the answer to part A, that number is multiplied by 4.186e-9 (the found k in seconds instead of years) in order to get the answer in Bq.

Help please :)

I would tackle this in this way
In 1 half life, half of the atoms will decay. If we start with 2.98 mg we know that in 5.26 years 1.49mg will decay and 1.49mg will remain
(5.26 x 365 x 24 x 60) sec ......> 1.49mg will decay
43.3 s                            .......> ?
This will give the mass of Co that will decay in 43.3s.
You will then need to convert this into moles (/60).
Each mole that decays released 1 mole (6.02?x 10^23) beta particles (electrons)
You can then find the number. Use your own date for N.
I am not familiar with the k you mention. Please check my method but I think it is ok

I'm still not getting the correct answer... any other suggestions?

I'm away from home with a pocketsurfer and no calculator. One thing I've noticed
is that whe you've found the mass of Co decayed in 43.3 s you will need
to change this into grams (/1000) before dividing by 60 to find the
number of moles of Co that decayed. This should be the same number
of moles of beta particles. Hope this helps.

I think (5.26 x 365 x 24 x 60) sec ......> 1.49mg will decay needs another x60 because at that point you are in minutes, not seconds. I'll wait until you get home so we can solve this problem together. Thanks a bunch btw.

you need to multiply the time conversion by another 60 to make it seconds

I'm still not getting the correct results. Can anyone assist me?