Question

The lone valence electron of sodium (n=3) will have which set of quantum numbers?

a) {n=3, ℓ=2, m_s=0, m_s=+1/2}
b) {n=3, ℓ=3, mₗ=0, m_s=+1/2}
c) {n=3, ℓ=0, m_s=0, m_s=+1/2}
d) {n=3, ℓ=1, m_s=0, m_s=+1/2}

Answer 1

The correct set of quantum numbers for the valence electron of sodium in the n=3 energy level is {n=3, ℓ=0, m₍=0, mₛ=+1/2}. This corresponds to the electron being in the 3s orbital, which is the lowest energy subshell available at that energy level.

Step-by-step explanation:

The lone valence electron of sodium (Na) in the n=3 energy level will have a specific set of quantum numbers associated with it. The principal quantum number (n) is already given as 3, which indicates the third energy level. The angular momentum quantum number (ℓ) for an s orbital is 0 since the s orbital is the first and only subshell in that principal energy level to be filled. The magnetic quantum number (m₍) for an s orbital can only be 0 because s orbitals are spherical and have no magnetic orientation. Finally, the spin quantum number (mₛ) can be either +1/2 or -1/2. In the case of sodium, which has an unpaired electron in its valence shell, we often assign a +1/2 value by convention.

Therefore, the correct set of quantum numbers for the valence electron of sodium in the 3s orbital is {n=3, ℓ=0, m₍=0, mₛ=+1/2}, which corresponds to option c).