Final answer:
Schrodinger's analysis of the hydrogen atom requires three quantum numbers: principal, azimuthal, and magnetic. These numbers provide information about the energy, size, shape, and orientation of the electron's orbital.
Step-by-step explanation:
In Schrodinger's analysis of the hydrogen atom, a total of three quantum numbers are needed. These quantum numbers include the principal quantum number (n), the azimuthal quantum number (l), and the magnetic quantum number (m). Each quantum number represents a different characteristic of the electron's motion in the atom.
The principal quantum number (n) determines the energy and size of the electron's orbital. The azimuthal quantum number (l) specifies the shape of the orbital (s, p, d, etc.), and the magnetic quantum number (m) determines the orientation of the orbital in space.
By using these three quantum numbers, Schrodinger's analysis provided a more comprehensive understanding of the hydrogen atom and was able to explain the behavior of electrons in larger atoms as well.