Calculating Total Energy of an Electron Orbiting a Hydrogen Nucleus

In summary, the total energy of an electron orbiting a hydrogen nucleus can be calculated by combining the kinetic and potential energy equations. The resulting equation is Etotal = -e^2/ 8ε0 π r, where e is the magnitude of the electron's charge and r is the orbital radius. The negative sign in the equation indicates that the energy is negative, which means it is bound to the nucleus. The minus sign in the potential energy expression (-ke^2/r) should not be considered, as it is a force expression and not an energy expression.
  • #1
Clara Chung
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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
 
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  • #2
Clara Chung said:
mv^2/r = -ke^2/r^2
Is the left hand side there positive or negative? What about the right hand side?
 
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  • #3
haruspex said:
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
 
  • #4
Clara Chung said:
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.
 
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  • #5
haruspex said:
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?
 
  • #6
Clara Chung said:
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.
 
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What is electrical potential energy?

Electrical potential energy is the energy that an object possesses due to its position in an electric field. It is a type of potential energy that is stored within an electrically charged object.

How is electrical potential energy calculated?

The formula for calculating electrical potential energy is: PE = qV, where PE is the potential energy, q is the charge of the object, and V is the electric potential. The unit for electrical potential energy is joules (J).

What factors affect the amount of electrical potential energy?

The amount of electrical potential energy is affected by the magnitude of the electric charge, the distance between the charged objects, and the strength of the electric field.

Can electrical potential energy be converted into other forms of energy?

Yes, electrical potential energy can be converted into other forms of energy such as kinetic energy or thermal energy. For example, when a charged object moves through an electric field, its potential energy is converted into kinetic energy.

What is the difference between electrical potential energy and electric potential?

Electrical potential energy is the energy stored within an electrically charged object, while electric potential is the potential energy per unit charge at a given point in an electric field. In other words, electric potential is a measure of how much potential energy an object has per unit charge.

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