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.

explanation:

let the different atoms be x and y. each with four protons and same mass will be represented as follows.

mass number is number of protons + number of neutrons.

            and  

since, it is given that one has a negative charge while the other is neutral. therefore, there will be increase in number of protons and the atom will be represented as follows.

according to periodic table, mass number of beryllium is 9 and it has atomic number 4 so, the atoms will be and .  

the protons and neutrons will be located inside the nucleus whereas the electrons will be revolving around the nucleus.