This requires more knowledge about atomic structure in multielectron atoms. Still, we duplicate the logic from hydrogen atom.
Now, let's get back to hydrogen atom, we know that energy of hydrogen atom is

for

Now, for inner most level, the electron in nickel's atom "sees" an effective nuclear charge of approximately

, where

is elementary charge and

is the atomic number of the element. This is because there are two electrons in the deepest shell. One will see nucleus and another electron be an effective nucleus. If you remember Bohr's theory and how to derive energy levels, you should notice that the charge of nucleus appears as square in the energy term. So, the energy is revised to

for

Now, in order to produce x-rays in the K series, i.e., x-rays from transition of n=1 level, the minimum energy is from transition from n=1 to the closest level, n =2.

Plugging

, we got

The correct is therefore (D). 28 of 100 people got the right answer.