Answer
When the potential difference is doubled, the energies of the characteristic x-rays are doubled.
Work Step by Step
We can write an expression for the original energy:
$E_1 = q~\Delta V_1$
We can write an expression for the energy when the potential difference is doubled:
$E_2 = q~\Delta V_2$
$E_2 = q~(2\times \Delta V_1)$
$E_2 = 2~q~\Delta V_1$
$E_2 = 2~E_1$
When the potential difference is doubled, the energies of the characteristic x-rays are doubled.
