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*10^.11m. What is the change in EPE(electric potential energy)?
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The PE at infinity is zero. THe PE at r is Vq which is equal to q^2/r Watch units.
To find the change in electric potential energy (EPE), you need to calculate the initial and final EPE, and then find the difference between them.
The formula for EPE between two charges is given by:
EPE = k * (q1 * q2) / r
where k is the electrostatic constant (approximately 9 x 10^9 N*m^2/C^2), q1 and q2 are the magnitudes of the charges, and r is the distance between the charges.
In this case, the electron and the proton form a hydrogen atom. 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. The distance between them is given as 5.29 x 10^-11 m.
Therefore, the initial EPE is when the electron and proton are infinitely far apart, which is effectively zero.
The final EPE can be calculated using the given values.
EPE = (9 x 10^9 N*m^2/C^2) * [(-1.6 x 10^-19 C) * (+1.6 x 10^-19 C)] / (5.29 x 10^-11 m)
Simplifying the expression:
EPE = (9 x 10^9 N*m^2/C^2) * (-2.56 x 10^-38 C^2) / (5.29 x 10^-11 m)
EPE = -1.18 x 10^-18 J
Therefore, the change in EPE is the difference between the initial and final EPE, which is:
Change in EPE = Final EPE - Initial EPE
= (-1.18 x 10^-18 J) - 0
= -1.18 x 10^-18 J
Hence, the change in electric potential energy is -1.18 x 10^-18 Joules.