The solution to the hydrogen atom Schrodinger Equation leads to a wavefunction with a dependence on three quantum numbers.
The solution to the hydrogen atom Schrodinger Equation leads to a wavefunction with a dependence on three quantum numbers n, \(l\) and \(m_l\).
It is difficult to visualize the complete hydrogen wave function, or orbital, because the wave function depends on three variables. For this reason, the wavefunctions are commonly separated into radial and angular portions.
The radial portion of the wavefunction depends on both n and \(l\) . \(l\) tends to be the quantum number that is associated with the shape of the orbital. The angular portion of the wavefunction depends on \(m_l\). \(m_l\) attributes to the degeneracy of the orbitals. There are \(2l+1\) possible values for \(m_l\), therefore, there are \(2l+1\) degenerate orbitals.
Associated with shape is the number of nodes present in a particular orbital. There are n-1 total nodes. These nodes are distributed between angular and radial nodes. Angular nodes are planes separating the orbital and attribute \(l\) nodes. Therefore, there are \(n-l-1\) radial nodes. The \(l\) quantum number is commonly expressed by a letter when describing the shape.
An NSF funded Project