Write a balanced half-reaction describing the reduction of aqueous vanadium(v) cations to aqueous vanadium(i) cations.

Reduction refers to a chemical reaction in which electrons are gained by one of the atoms involved in the reaction and at the same time lowering of an oxidation state of that atom takes place.  

In the given case, the reduction occurs at the cathode. In aqueous, V (vanadium) is present in +5 oxidation state that on reduction modifies to vanadium (aq) with +1 oxidation state.  

The half reaction is:  

V⁵⁺ (aq) + 4e⁻ → V¹⁺ (aq)

explanation:

let the different atoms be x and y. each with four protons and same mass will be represented as follows.

mass number is number of protons + number of neutrons.

            and  

since, it is given that one has a negative charge while the other is neutral. therefore, there will be increase in number of protons and the atom will be represented as follows.

according to periodic table, mass number of beryllium is 9 and it has atomic number 4 so, the atoms will be and .  

the protons and neutrons will be located inside the nucleus whereas the electrons will be revolving around the nucleus.