Physics MCQ

When accelerating an object across a potential difference, the total amount of energy gained is the same for an object of a constant charge, regardless of mass.

To show this, suppose we accelerate an object of charge $q$ and mass $m$ across a P.D $V$. The energy gained is $q\times V$. As you can see, nowhere is the mass used in the equation. Furthermore $\lambda = \frac{E}{hc}$, and as energy is not dependent on mass, neither is the wavelength.