How many electrons in a multi-electron atom could identified by the two quantum numbers n = 2, ms = +1/2?

The number of electrons that can have the quantum numbers n = 2 and mₛ = +1/2 in a multi-electrons atom is 4.

Explanation:

The quantum number n stands for the principal number and it indicates an electron's shell in an atom.

Shells K, L, M, N, O have principal quantum numbers 1, 2, 3, 4, 5 respectively. So, n = 2 represents the L-shell whose maximum number of electrons is given by a general formula, 2n² = 2 (2²) = 8 electrons.

The mₛ represents the spin quantum number which indicates the direction of spin of electrons in the sub-orbital of atoms. It is usually of 2 types, clockwise and anti-clockwise spin. The numbers (-1/2) and (+1/2) are values used for specifying this direction of spin.

So, in the L-shell with 8 maximum number of electrons, half of the electrons in their respective sub-orbital will spin in the clockwise direction (i.e. 4 electrons) and the other half will spin in the anti-clockwise direction (i.e. 4 electrons); half of them will have spin quantum number of (+1/2) and the other half will have spin quantum number of (-1/2) in their respective sub-orbitals.

The number of electrons that can have the quantum numbers n = 2 and mₛ = +1/2 in a multi-electrons atom is 4.