Question

The quantum numbers for the outermost electron of Aluminium are 
1. n = 3, l = 1, m_l = -1, s = +1/2
2. n = 4, l = 1, ml = -1, s = +1/2
3. n = 3, l = 0, ml = 0, s = +1/2
4. n = 3, l = 2, ml = -1, s = +1/2

Answer 1

Correct Answer - Option 1 : n = 3, l = 1, m_l = -1, s = +1/2

Concept:

The four quantum numbers are used to describe the probable location of an electron in an atom.

Principal Quantum Number: The first quantum number describes the electron shell, or energy level, of an atom. The value of n ranges from 1 to the shell containing the outermost electron of that atom.

Azimuthal Quantum Number: The second quantum number, known as the angular or orbital quantum number, describes the subshell and gives the magnitude of the orbital angular momentum through the relation. The value of l ranges from 0 to n – 1.

Magnetic Quantum Number: The magnetic quantum number describes the energy levels available within a subshell and yields the projection of the orbital angular momentum along a specified axis. The values of ml range from –l to +l, with integer steps between them.

Spin Projection Quantum Number: The fourth quantum number describes the spin (intrinsic angular momentum) of the electron within that orbital and gives the projection of the spin angular momentum (s) along the specified axis.

An electron has spin s = ½, consequently ms will be ±, corresponding with spin and opposite spin. Each electron in any individual orbital must have different spins because of the Pauli Exclusion Principle, therefore an orbital never contains more than two electrons.

Explanation:

Given outermost electron of aluminium,

The electronic configuration of aluminium is 1s² 2s² 2p⁶ 3s² 3p¹

The outermost electron will have the configuration 3p¹;

3p¹ ⇒ n = 3, l = 1 (p), m_l = -1 (p_x orbital), s = +1/2;

⇒ Set of quantum numbers = (3, 1, -1, +1/2)