# Deriving equation of potential energy of H2

• zimo123
In summary, to derive the equation for the potential energy of a system of 2 hydrogen atoms, one can use the Schrodinger equation and take into account the electron/electron, nucleus/nucleus, and electron/nucleus interactions. The resulting equation is V(R) = \frac{e^2}{2\pi\epsilon_0 R} and can be graphed to show the potential energy as a function of the internuclear distance.
zimo123

## Homework Statement

Derive the equation for the potential energy of a system of 2 hydrogen atoms as a function of internuclear distance.

## Homework Equations

For electron/electron and nucleus/nucleus repulsion:

$V_E=\frac{e^2}{4\pi\epsilon_0 R}$

For electron/nucleus attraction:

$V_E=-\frac{e^2}{4\pi\epsilon_0 R}$

Schrodinger equation:

$-\frac{\hbar^2}{2m}\frac{\partial^2\psi (R)}{\partial R^2}+V(R)\psi (R)=E\psi (R)$

## The Attempt at a Solution

I am really confused on what to take for V(R) ? There are 4 electric interactions (2 electrons and 2 positively charged nuclei). Also, I don't understand what I should graph, is it the wave function ? If someone could just give me a little hint, it would help a lot!

Thank you so much

for your question. The potential energy of a system of 2 hydrogen atoms can be derived using the Schrodinger equation. In this case, V(R) would represent the total potential energy, which is the sum of the electron/electron, nucleus/nucleus, and electron/nucleus interactions. Therefore, the equation for the potential energy of a system of 2 hydrogen atoms as a function of internuclear distance (R) would be:

V(R) = \frac{e^2}{4\pi\epsilon_0 R} + \frac{e^2}{4\pi\epsilon_0 R} - \frac{e^2}{4\pi\epsilon_0 R} = \frac{e^2}{2\pi\epsilon_0 R}

To graph this potential energy, you would plot V(R) on the y-axis and the internuclear distance (R) on the x-axis. The resulting graph would show the potential energy as a function of the internuclear distance, giving you an idea of the stability of the system at different distances.

I hope this helps clarify the concept for you. Good luck with your studies!

## 1. What is the equation for potential energy of H2?

The equation for potential energy of H2 is given by U(r) = -kQq/r, where k is the Coulomb's constant, Q and q are the charges of the two hydrogen atoms, and r is the distance between them.

## 2. How is the equation derived?

The equation for potential energy of H2 is derived from the electric potential energy formula, U = kQq/r, by considering the system of two hydrogen atoms as a point charge interacting with each other through the electrostatic force. By using the definition of electric potential energy, the equation can be derived.

The negative sign in the equation for potential energy of H2 represents the attractive nature of the electrostatic force between the two hydrogen atoms. It indicates that the system of two atoms has a lower potential energy when they are closer together, due to the attractive force between them.

## 4. What are the units of the equation?

The units of the equation for potential energy of H2 are joules (J) for energy, coulombs (C) for charge, and meters (m) for distance. This equation is derived from the SI (International System of Units) units for energy and force.

## 5. How is this equation used in practical applications?

The equation for potential energy of H2 is used in various fields of science and engineering, such as chemistry, physics, and material science. It is used to understand the behavior of molecules and chemical reactions, and to calculate the energy required to break or form chemical bonds. In engineering, this equation is used to design and optimize electrostatic systems, such as capacitors and electric motors.

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