Chapter 32 - Nuclear Physics and Nuclear Radiation - Problems and Conceptual Exercises - Page 1154: 58

$110rad$

We can find the required radiations of protons as follows: $Dose\space in\space rad(proton)=\frac{dose\space in \space rad(\alpha \space particle)\times RBE(\alpha \space particle)}{RBE(proton)}$ We plug in the known values to obtain: $Dose\space in\space rad(proton)=\frac{55\times 20}{10}=110rad$