Work Done and Potential Energy in Electrostatics This is a question from class 12 Physics NCERT Part 1:

I am having so much trouble with this, I can't figure out where I'm going wrong. I solved part (a) here:

(a) U= -27.2 eV
(b) Here, the kinetic energy is given to be half of the potential energy, and kinetic energy is always positive, therefore, K= +13.6 eV 
Total energy= -27.2 +13.6 = -13.6 eV
Now this is where I'm going wrong. 
To free an electron, the final potential energy must be zero and also work done is change in potential energy. 
From that, W= 0- (-27.2) = +27.2 eV. But the answer is +13.6 eV according to my book. What am I doing wrong?
(c) In this part,
U= (U at 0.53 Å) – (U at 1.06 Å)
U= -27.2 eV -(-13.6eV)
U= -13.6 eV
therefore,
K= +6.8 eV
and,
Total energy= -13.6 +6.8 = -6.8 eV
But my book says that the total energy here is zero. How?
Sorry for this long question, but I've been trying to solve this for so long. Any help is appreciated. Thank you so much.
 A: *

*To free an electron (or any particle), the requirement is that the particle should be able to run off to indefinitely large distances. This means that the electron should have sufficient kinetic energy so that it can fight against the potential and reach the spatial infinity. Thus, the electron should at least have as much kinetic energy as the difference between the potential at its initial position and the potential at the spatial infinity. If you take the reference point (datum) for your potential at spatial infinity then this means that the total energy of the particle should be greater than or equal to zero. So, since the total energy of the electron in your case is $-13.6$ $\text{eV}$, you have to at least provide it $13.6$ $\text{eV}$ energy so as to make its total energy non-negative. 

*Why would change in the reference point for your potential energy change the kinetic energy of the electron? The kinetic energy is a physical quantity, the reference point for the potential is of no physical significance in itself. You can set it anywhere you want--the kinetic energy would remain the same. The reference point of the potential energy is simply a figment of the imagination of the physicist, a very useful one, but purely non-physical. Following the same logic, changing your reference point shouldn't change anything about how much energy is required to set the electron free. 
