Answer
a). 30.6 GeV,
b). 8.0 GeV.
Work Step by Step
a). Mass of alpha particle can be calculated by subtracting 2 electron masses from the $He_{2}^{4}$ atomic mass :-
$=4.001506u$.
Then $mc^{2}=(4.001506u)\times(931.5MeV/u)=3.727GeV.$
Now, masses of target and projectile particles are equal, so
$E_{a}^{2}=2mc^{2}(E_{m}+mc^{2})$
$Since, E_{a}^{2}=16 GeV, E_{m}=30.6 \,GeV$,
b). Each beam must have $\frac{1}{2}E_{a}=8.0\,GeV.$