Answer
(a) an electron with a total energy of $1000MeV$
Work Step by Step
Total energy $E=vmc^{2}=vEo$
$v=\frac{E}{Eo}$
Electron's rest energy is $Eo=0.511MeV$. When its total energy is $1000MeV$ the value of $v=\frac{1000MeV}{0.511MeV}\approx1957$
Proton's rest energy is $Eo=938MeV$. When its total energy is $1000MeV$ the value of $v=\frac{1000MeV}{938MeV}\approx1.07$
Neutron's rest energy is $Eo=939MeV$. When its total energy is $1500MeV$ the value of $v=\frac{1000MeV}{939MeV}\approx1.6$
The value of $v$ is more for electron with total energy of 1000MeV. So, its speed is more as compared to other 2 particles. (a) is the answer.
