Don’t worry: you don’t need to memorize this equation. What’s worth noting for the
purposes of SAT II Physics is that there are certain constant values for r, for different
integer values of n. Note also that r is proportional to , so that each successive radius is
farther from the nucleus than the one before.
Electron Potential Energy
The importance of the complicated equation above for the radius of an orbiting electron
is that, when we know the radius of an electron, we can calculate its potential energy.
Remember that the potential energy of an electron is. If you plug in
the above values for r, you’ll find that the energy of an electron in a hydrogen atom at its
ground state (where n = 1 and Z = 1 ) is –13.6 eV. This is a negative number because we’re
dealing with potential energy: this is the amount of energy it would take to free the
electron from its orbit.
When the electron jumps from its ground state to a higher energy level, it jumps by
multiples of n. The potential energy of an electron in a hydrogen atom for any value of n
is: