# Change in Electric potential, potential energy, and work problem.

## Homework Statement

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?

## Homework Equations

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.

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TSny
Homework Helper
Gold Member
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.
That looks good.

To find work needed to move up, I need the electric potential "difference" from the outer electron to the next level multiplied by a -q to get potential energy.
My interpretation of the question is that you want to remove the outer electron all the way to infinite distance from the atom, rather than to the next energy level. But the question statement is not very clear.

(intuitively I know that potential energy will be positive and work will be negative; therefore the work applied must be positive.)
Be careful with the signs. Note that you are asked to find the work you would have to do to remove the electron (not the work done by the electric force).

Dear Tsny,

The only way to find work is to know the change in electric potential, and the work applied would be the -of the work done by the electric field. I agree, this question is vague. If it were to move an infinite distance from the atom, how would I use that to get the right answer?