Question

Why should it take significantly more energy to move a beam of alpha particles than a beam of beta minus (β–) particles?

Answer 1

An 'alpha particle' is the same thing as the nucleus of a helium atom ... 
a little bundle made of 2 protons and 2 neutrons.

A 'beta' particle is an electron.

The mass of an alpha particle is more than 7,000 times the mass of 
an electron, so it certainly takes more energy to get it moving.

Answer 2

because the mass of an alpha particle is significantly greater than the mass of a beta particle