Imagine a lithium atom where the two electrons in the first orbital are at exact opposite sides of the nucleus and the electron in the second orbital is in line with the other electrons so that the three electrons and the nucleus all lie on a straight line. How much work would you need to apply to remove the outer most electron if the atomic radius is 100picometer and the distance between the first and second orbital is 50picometer?
The answer is (kq^2/300)*10^12J.
Based on the principle of superposition, I can find the electric potential at the outermost electron for lithium. (-kq)/50*10^-12+(3kq)/100*10^-12+(-kq)/150*10^-12 where k is the constant and a a is the type of charge.
The potential I find is then kq/300*10^-12.
To find work needed to move up, I need the electric potential "difference" from the outer electron to to the next level multiplied by a -q to get potential energy.(intuitively I know that potential energy will be positive and work will be negative; therefore the work applied must be positive.)
I don't know how the book just found this potential difference and ultimately the answer choice.
I have this feeling that the book left out information to the point that this problem is impossible to solve.