Calculating Total Energy of an Electron Orbiting a Hydrogen Nucleus

[Clara Chung]

Homework Statement

Prove that the total energy of an electron orbiting a hydrogen nucleus is Etotal = -e^2/ 8ε0 π r where e is the magnitude of charge of an electron and r is the orbital radius.

Homework Equations

Knowledge

The Attempt at a Solution

Here is my attempt:
For KE,
mv^2/r = -ke^2/r^2
mv^2/2 = -ke^2/2r

For PE,
PE= k(-e)e/r - k(-e)e/∞
=-ke^2/r
KE+PE =-3e^2/ 8ε0 π r ,why am I wrong? please help

 

[haruspex]

mv^2/r = -ke^2/r^2

Is the left hand side there positive or negative? What about the right hand side?

 

[Clara Chung]

Is the left hand side there positive or negative? What about the right hand side?

LHS is positive and RHS is negative? They should both be positive as the negative sign represents the direction?I don't get it

 

[haruspex]

LHS is positive and RHS is negative? I don't get it

So the right hand side must be wrong. Try explaining in detail how you arrive at the minus sign there.

 

[Clara Chung]

So the right hand side must be wrong. Try explaining in detail how you arrive at the minus sign there.

Thanks for helping me. But why the minus sign in potential energy need not to consider?

 

[haruspex]

Thanks for helping me. But why the minus sign in potential energy need not to consider?

That is not an energy expression, it's a force expression.