Answer
Absorbed dose
$D = 1.057 \space Gy = 105.7 \space rad$
Equivalent dose
$2114 \space rem = 21.14 Sv$
Work Step by Step
To find how the number of $\alpha$ particles absorbed, we use the following equation
$ n = (0.72 \times 10^{-6} Ci) (3.70\times 10^{10} s^{-1}Ci^{-1})(3.16 \times 10^{7} s) $
$ n = 8.42 \times 10^{11}$
Energy absorbed by the person $E = mD$ Here we solve for D to find the dose.
$D = \frac{E}{m}$
$D = \frac{(8.42 \times 10^{11})(4.0 \times 10^6 eV) ( 1.6 \times 10^{-19} J/eV)}{0.51 kg}$
$D = 1.057 \space Gy = 105.7 \space rad$
The equivalent dose is
$(RBE)(D) = (20)(105.7 \space rad) = 2114 \space rem = 21.14 Sv$
