quantum numbers

what is n

the principal quantum number

what is l (lowercase L) what does it determine

orbital angular momentum quantum number (or azimuthal quantum number)

determines the shape of an atomic orbital by giving the number of nodal planes in each orbital type (as orbitals change phase at their nodal planes)

value of l (L) for s, p and d orbitals

s: l = 0

p: l = 1

d: l = 2

what is m_l and what does it determine

magnetic quantum number

determines the direction of an atomic orbital

value of m_l for s, p, d and what values can it take

can take the values: -l, (-l+1), …, (l-1), l

s (l = 0): m_l = 0 only (spherical so no preferred direction)

p (l = 1): m_l = -1, 0 or 1

d (l = 2): m_l = -2, -1, 0, 1 or 2

s, p, d orbitals for each shell n

1 s orbital, 3 p orbitals when n ≥ 2, 5 d orbitals when n ≥ 3

what is m_s and what does it determine

spin magnetic quantum number

each orbital can hold up to 2 electrons, which are distinguished by their spin. m_s describes their spin.

what values can m_s take and what do they mean

electrons can spin in one of two directions, termed up (m_s = +0.5) and down (m_s = -0.5)