Significance of quantum numbers to an electron in an atom:**

Here are the answers to your questions:

• Significance of quantum numbers to an electron in an atom: Quantum numbers are a set of four values that completely describe the unique quantum state of an electron in an atom. They specify the electron's energy level, the shape of its orbital, its spatial orientation, and its spin.

  • The principal quantum number ($n$) indicates the electron's main energy level and average distance from the nucleus.
  • The azimuthal (or angular momentum) quantum number ($l$) describes the shape of the electron's orbital (e.g., s, p, d, f).
  • The magnetic quantum number ($m_l$) specifies the orientation of the orbital in space.
  • The spin quantum number ($m_s$) describes the intrinsic angular momentum (spin) of the electron.

• Two (2) limitations of J. J. Thomson's atomic model:

  1. It failed to explain the results of Rutherford's gold foil experiment, which demonstrated that the positive charge and most of the mass of an atom are concentrated in a tiny nucleus, not spread uniformly.
  2. It could not explain the stability of an atom or the origin of the discrete line spectra observed for elements.