Question

Does the following quantum numbers exist? If not, explain why.

n = 5, l = 3, m_l = 2, m_s = + ½   - ________________________________

n = 6, l = -2, m_l = 1, m_s = - ½ - ________________________________

n = 3, l = 1, m_l = -1, m_s = - ½ - ________________________________

Answer 1

FIRST, the principal quantum number ["n"] relates to the "shell" and energy of the orbital.

SECOND, the angular momentum quantum number ["ℓ"], tells you how many angular nodes exist. These are planes (or cones) which go through nucleus, and which define places in space where the electron can and cannot exist. The possible values (orbitals) are limited by the principal quantum number, according to the formula: ℓ = 0,1... n-1

THIRD, the magnetic quantum number, ["mℓ"],  as a directional quantum number, which defines which way an electron's orbital can point. The rule says that mℓ values can range from +ℓ to -ℓ

FOURTH, the spin quantum number, or ["ms"], which defines the spin of an electron. Two electrons can share the same orbital only if they have different spins, according to the Pauli Exclusion principle. Electron spin can either be +½ or -½.

On the basis of above description it's obvious that the quantum number shown by 2( n=6, l=-2, ml=1, ms=-1/2) is not valid as value of can not be 0.

Remaining two are valid quantum numbers.