Activity (A) of an element is related to the number of atoms of that element N as follows:
A = k*N --------(1)
k = rate constant = 0.693/t1/2--------(2)
N = # moles of that element * Avogadro's number Na
For Sr: t1/2 = 28.8 yr
A(Sr) = 0.693/28.8 * N(Sr) = 0.0241 * N(Sr)
A(Sr) = 0.0241*(mass Sr/90)*Na= 0.000268 *mass Sr *Na ------------(3)
For Co : t1/2 = 5.26 yr
A(Co) = 0.693/5.26 *N(Co) = 0.1317 *N(Co)
A(Co) = 0.1317 * (1/60)*Na = 0.00219 * Na -------(4)
It is given that:
A(Sr) = A(Co)
0.000268 *mass Sr *Na = 0.00219 * Na
mass Sr = 0.00219/0.000268 = 8.17 g