Which of the following quantum numbers are correct for the outermost electron of sodium atom? (a) \(n=4, l=0, m=0, s=+1 / 2\) (b) \(n=3, I=0, m-0, s--1 / 2\) (c) \(n=3, l=1, m=+1, s=+1 / 2\) (d) \(n=3, l=2, m=-1, s=-1 / 2\)

Understanding electron configuration is crucial when studying the properties of atoms. For sodium, which has 11 electrons, the configuration follows a specific pattern according to the periodic table. Most importantly, the electron configuration is written using the principle of lowest energy filling first.

The electron configuration starts at the lowest energy levels: 1s, 2s, then moves through the various p, d, and f orbitals corresponding to the increasing principal quantum number, n. Within each energy level, electrons fill the s orbital first, then p, and so forth, following the pattern outlined by the Aufbau principle. Moreover, each orbital can only hold a certain number of electrons (for instance, s orbitals can hold 2), which further dictates how these electrons are organized.

• 1s can hold two electrons
• 2s is next, also holding two
• When we reach 3s (where sodium’s outermost electron resides), it holds one electron

In the case of sodium’s outermost electron, the correct electron configuration is 3s¹, which directs us to the other quantum numbers for a full description.

The azimuthal quantum number (), also known as the angular momentum quantum number, signifies the subshell or type of orbital where an electron can be found. It is integral to determining the shape of the orbital and has values that range from 0 to - 1. These numbers correspond to the s, p, d, and f orbitals, with s being 0, p being 1, d being 2, and f being 3.

For the sodium atom's outermost electron, which is in the 3s orbital, the azimuthal quantum number is 0, since s orbitals are spherical in shape and are the first in the sequence of orbital shapes within any principal energy level.

The magnetic quantum number (m) provides information about the orientation of an orbital within a subshell and indirectly relates to the magnetic field the electron may experience. It can take on any integral value between - and +, including zero. For s orbitals, however, because they are spherically symmetrical, this number is always 0, reflecting that the s orbital has only one orientation in space.

Thus, for sodium’s 3s electron, the magnetic quantum number is indeed 0. This value is critical for fully understanding and predicting the behavior of electrons within a magnetic field, which directly correlates with their spatial orientation.

Finally, the spin quantum number (s) describes the intrinsic angular momentum of an electron, essentially its 'spin'. Electrons act as if they are spinning on an axis and can have one of two possible spins: +1/2 or -1/2. This quantum number is fundamental in explaining the Pauli Exclusion Principle, which states that no two electrons in an atom can have the same set of four quantum numbers.

Since the 3s orbital in sodium has only one electron, it can exhibit either spin. In practice, this means that either +1/2 or -1/2 is acceptable when we are talking about a solitary electron in an orbital, as long as the electron does not share the same four quantum numbers as another electron within the atom.