[sugarwink]

You want to do an experiment using 47Ca (half-life=4.53 days). You will need 3.80 μg of the nuclide. What mass of CaCO3 (100% enriched in 47Ca) must you order if it will take 33 hours to be delivered to you from the nuclear facility where it is prepared?

time of transport / half life = n
33 hrs / 108.72 hrs = n
n = 0.303432009

1/2^n = x
x = 0.810266271

This is how far I've gotten, where am I suppose to go from here?

[Schrödinger]

Using the half-life data, find out the rate constant for the decay of ⁴⁷Ca.
Then, use the first order integrated rate equation, with the unknown being the initial mass (or equivalently, moles).

For the rate equation :
k,t (33 hrs) and final mass (3.80 μg) are known. All you have to do is find the initial mass.

[sugarwink]

t1/2 = ln(2) / k
108.72hrs = ln (2) / k
k = 0.006375526

ln(N/Ninitial) = - kt
ln(3.80μg/Ninitial) = - (0.006375526)(33hrs)
Ninitial = 4.69μg

Where am I going wrong? I am still confused.

[Borek]

4.69 μg looks OK to me, but so far it is a mass of nuclide - that's not what you order.