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 5.29 x 10 -11 m. what is EPE final - EPE initial, which is the change in the electric potential energy?
The electrical potential energy is a negative number,
-k e^2/a
where a is the orbit radius (which you have been given), e is the electron (and proton) charge, and k is the Coulomb's Law constant.
To find the change in electric potential energy (EPE) between the initial state and the final state, you need to calculate the EPE in both situations and then subtract the initial EPE from the final EPE.
The formula to calculate the electric potential energy between two charges is:
EPE = (k * q1 * q2) / r
where:
- EPE is the electric potential energy
- k is the Coulomb's constant (9 x 10^9 Nm^2/C^2)
- q1 and q2 are the magnitudes of the charges
- r is the distance between the charges
In the initial state, the electron and proton are effectively an infinite distance apart, so the electric potential energy in the initial state is considered to be zero (EPE initial = 0).
In the final state, the electron orbits the proton at an average distance of 5.29 x 10^(-11) m. Since the hydrogen atom consists of one electron and one proton, we can use the given values in the formula to calculate the EPE final.
EPE final = (k * q_electron * q_proton) / r
To get the values of the charges, we know that the charge of an electron is -1.6 x 10^(-19) C, and the charge of a proton is +1.6 x 10^(-19) C (they have equal magnitudes but opposite signs).
Substituting the values into the formula:
EPE final = (9 x 10^9 Nm^2/C^2 * (-1.6 x 10^(-19) C) * (1.6 x 10^(-19) C)) / (5.29 x 10^(-11) m)
Calculating this expression will give you the value of EPE final.
Finally, you can find the change in electric potential energy by subtracting the initial EPE (zero) from the final EPE:
EPE final - EPE initial = EPE final - 0 = EPE final