Answer
1.4 days.
Work Step by Step
Assume that the decay rate is constant during the treatment. Calculate the time to administer 32 Gy.
We are told that 1.0 mCi delivers about 10 mGy/min.
In that case, the 1.6 mCi source that we are provided would deliver 16 mGy/min.
$$dose=rate\times time$$
$$time=\frac{dose}{rate}=\frac{32\;Gy}{0.016Gy/min}\frac{1\;day}{1440min}=1.4\;days$$
Our calculated time is short compared to the 14.3-day half-life of the P-32 isotope, so our original assumption of a constant decay rate is reasonable.
