Answer
$\rm 2.13\;\rm mCi$
Work Step by Step
We need to find the number of nuclei in order to be able to find the initial activity of $\rm Tc$;
We know that gammas' RBE factor is 1,$\rm (50\; mrem= 50\; mrad)$.
Noting that the number of $\rm Tc$ affecting the man is twice the number produced.
$$N_{\rm Tc}=2\times\rm 50\times 10^{-3}\;rad \times \dfrac{1\;rad\cdot 55\;kg }{100\;kg}\times\dfrac{1\;eV}{1.6\times 10^{-19}\;J\times 140\times 10^3\;eV}$$
$$N_{\rm Tc}= \bf 2.455\times10^{12}\;\rm nuclei$$
Thus the initial activity is given by
$$R=\lambda N=\dfrac{\ln 2}{T_{_\frac{1}{2}}}N$$
Plugging the known;
$$R= \dfrac{\ln 2}{ 6\times 60^2}\times2.455\times10^{12} =\bf 7.88\times 10^7\;\rm decay/s$$
which is equal to
$$R =\rm 7.88\times 10^7\;\rm decay/s\times \dfrac{1\;Ci}{3.7\times 10^{10}\;decay/s}=\color{red}{\bf 2.13} \;mCi$$
