[Biocheistry_97]

Hello,

How do I go about finding the relative difference in the electrostatic potential energy associated with the electron at its most likely position in a 1s orbital and in a 2s orbital?

I attempted to use:  E_1s = k ( q₁ x q₂ )/ r   and E_2s = k ( q₁ x q₂ )/ r , since the fractions can cancel, but did not know what the radius should be.

Thank you.

[mikasaur]

To what atom is this problem referring?

[Enthalpy]

Let's assume this atom has one electron.

One simpler way: the electrostatic energy is -2* the kinetic energy and their sum is the electron's energy. So as you know the energies of 1s and 2s and their difference, you know the difference in electrostatic energy too.

Now, if you stick to "likely positions", and without quibbling too much about the meaning...

1s and 2s have their biggest probability density per volume unit right at the nucleus. Pity, you can't compute an electrostatic energy there.

Since the wavefunction is fuzzy, it takes conventions to define mean radii. A possible one is to evaluate a probability to find the electron in any direction at a distance r to r+dr to the nucleus. This probability density is zero at the nucleus and has a maximum at a finite r, which you may use as some "mean distance" if you like.

You can find these radii somewhere on Wiki. Starting at the quantum atom should bring you there.