Potential energy problem. help >.<

[hichangkyu]

An electron and a proton are initially very far apart (effectively an infinite distance apart). They are then brought together to form a hydrogen atom, in which the electron orbits the proton at an average distance of 5.05e-11 m. What is EPEfinal - EPEinitial, which is the change in the electric potential energy?

Homework Equations

V=kq/r
PEfinal=qVfinal

The Attempt at a Solution

since initially, r was very big and V very small, you can consider the initial potential energy to be zero... right?

after that i calculated for V. V= (9.0e9)(-1.6e-19)/5.05e-11 = -28.5148.
what do i do from here? I multiplied by the charge of the electron again and got 4.5623e-18 but that's wrong?

any light that can be shed on this will be greaaaaaaaaatly appreciated. thanks!

 

[lippyka]

EPEfinal - EPEinitial = qVfinal, where q is the charge of the electron (-1.6e-19 C) and Vfinal is the electric potential at the average orbital distance of 5.05e-11 m. Therefore, the change in electric potential energy is: EPEfinal - EPEinitial = (-1.6e-19 C)(-28.5148 V) = 4.5623e-18 J

 

[baba89]

You are on the right track! Since the initial distance between the electron and proton was effectively infinite, the initial electric potential energy can be considered zero. Therefore, the change in electric potential energy is simply the final electric potential energy.

To calculate the final electric potential energy, we use the equation PEfinal=qVfinal. You have correctly calculated the electric potential Vfinal to be -28.5148 V. However, you need to use the charge of the electron (1.6e-19 C) instead of the proton's charge to calculate the final electric potential energy.

Therefore, the final electric potential energy is PEfinal=(1.6e-19 C)(-28.5148 V) = -4.5623e-18 J. This is the correct answer for the change in electric potential energy. I hope this helps!