Homework problem - MasteringPhysics.com (electric potential)

[adam32386]

In a semiclassical model of the hydrogen atom, the electron orbits the proton at a distance of 0.053nm.


What is the electric potential of the proton at the position of the electron?

What is the electron's potential energy?




(do i use the area on a circle in this equation? or is this an answer with constants in the solution?) if you guys could help me figure this out I would appreciate it.
thank you.

 

[hage567]

Start with this: what's the equation for electric potential due to a point charge?

 

[Moetasim]

The electric potential of the proton at the position of the electron can be calculated using the equation V = kQ/r, where k is the Coulomb's constant, Q is the charge of the proton, and r is the distance between the proton and electron. Plugging in the given values, we get:

V = (9x10^9 N*m^2/C^2)(1.6x10^-19 C)/(0.053x10^-9 m) = 2.86x10^9 V

This means that at a distance of 0.053nm, the proton has an electric potential of 2.86x10^9 volts.

To calculate the electron's potential energy, we can use the equation U = -kQq/r, where U is the potential energy, k is the Coulomb's constant, Q and q are the charges of the proton and electron respectively, and r is the distance between them. Plugging in the given values, we get:

U = -(9x10^9 N*m^2/C^2)(1.6x10^-19 C)(-1.6x10^-19 C)/(0.053x10^-9 m) = -4.86x10^-18 J

Therefore, the electron's potential energy is -4.86x10^-18 joules at a distance of 0.053nm from the proton. Note that this is a negative value, indicating that the electron has a lower potential energy when it is closer to the proton.