Answer
$1.58 \times10^{12}s$.
Work Step by Step
The mass of a single nucleus is $124m_p=2.07\times10^{-25}kg$.
Find the number of atoms, N, in 6.13g = 0.00613kg.
$$N=\frac{0.00613kg }{2.07\times10^{-25}kg }=2.96\times10^{22}$$
The rate of decays is $0.350Ci=1.295\times10^{10}Bq$.
Calculate the decay constant $\lambda=\frac{1.295\times10^{10}Bq }{2.96\times10^{22}}=4.39\times10^{-13}s^{-1}$
Finally, calculate the half-life.
$T_{1/2}=\frac{ln2}{\lambda}=1.58 \times10^{12}s$
