What is the principal quantum number and its properties? What is the angular momentum quantum number and its properties?

Here are the completed notes on quantum numbers:

• Principal Quantum Number ($n$)

  • Denoted by letter $n$.
  • It has integral values $1, 2, 3, \dots$.
  • Corresponds to Bohr's equation for energy: $E = -R_H \left(\frac{1}{n^2}\right)$
  • The principal quantum number relates to the energy level of an electron and the average distance of the electron from the nucleus (i.e., the size of the orbital).

• Angular Momentum Quantum Number ($l$)

  • Denoted by letter $l$.
  • This quantum number tells the shape of an orbital.
  • It depends on the value of the Principal Quantum Number ($n$).
  • For a given value of $n$, $l$ has possible integral values from $\boxed{0 \text{ to } n-1}$.