Up to ten electrons can share the quantum numbers n = 3 and L = 2, all residing in the five 3d orbitals with paired spins.
Can an electron have the quantum numbers n = 3, l = 2, and ml?
Yes — an electron can have n = 3, l = 2, and ml = −2; the only restriction is that no two electrons in the same orbital can share the same set of four quantum numbers.
That’s the Pauli exclusion principle at work — each orbital can only hold two electrons, and they need opposite spins. So for the orbital defined by n = 3, l = 2, and ml = −2, you’ll find one spin-up and one spin-down electron max.
How many orbitals can have the quantum numbers n = 3 and L = 2?
Five orbitals can share n = 3 and L = 2; these are the five 3d orbitals (dxy, dyz, dzx, dx²-y², and dz²).
You get five orbitals because the formula is 2l + 1 — plug in l = 2 and you land on five distinct orbitals, each with its own ml value. Simple math, really.
What subshell is described by the quantum numbers n = 3 and L = 2?
The subshell is 3d; when n = 3 and l = 2, the subshell is labeled “d” and is part of the third principal shell.
Here’s the naming pattern: 0 = s, 1 = p, 2 = d, 3 = f. So l = 2 always maps to a d-subshell. No surprises there.
How many electrons in an atom can have the quantum numbers n = 3 and L = 3?
Zero electrons can have n = 3 and L = 3, because the maximum value of l is n – 1 (so for n = 3, l can only be 0, 1, or 2).
Try setting l = 3 for n = 3 and you’ll hit a wall — the rule l ≤ n − 1 makes that combo impossible. End of story.
What are the four quantum numbers?
The four quantum numbers are n, l, ml, and ms, which specify an electron’s energy level, orbital shape, orbital orientation, and spin orientation.
Think of them as an electron’s full mailing address: n tells you the floor (shell), l the wing (subshell), ml the room number (orbital), and ms which twin is inside (spin up or down). Handy mental image, right?
What are the possible values of L when n = 4?
For n = 4, l can be 0, 1, 2, or 3, giving s, p, d, and f subshells respectively.
The allowed l values run from 0 up to n − 1, so 4 − 1 = 3 is the highest subshell letter you’ll see. No exceptions.
What is the shape of an orbital if the value of L = 2?
An orbital with l = 2 has a clover-leaf or double-dumbbell shape, commonly called “d-orbital” lobes.
Picture two dumbbells crossing at right angles — that’s your classic d-orbital look you’ll spot in chemistry textbooks. Honestly, this is the best way to visualize it.
What is the maximum number of electrons in n = 4, L = 3?
Fourteen electrons can occupy the n = 4, l = 3 subshell (the 4f subshell).
The 4f subshell has seven orbitals (2l + 1 = 7), each holding two electrons, for a total of 14. Math checks out.
How many electrons can n = 4 and L = 2 have?
Ten electrons can occupy the n = 4, l = 2 subshell (the 4d subshell).
Five orbitals in the 4d set, two electrons per orbital — 5 × 2 = 10 electrons max. That’s the capacity.
What subshells are possible in n = 3?
The possible subshells are 3s, 3p, and 3d.
For any principal quantum number n, the allowed subshells are s (l = 0), p (l = 1), … up to d (l = 2) when n ≥ 3. No curveballs here.
How many electrons in potassium have n = 3 and L = 0?
Two electrons occupy the n = 3, l = 0 level in a neutral potassium atom (atomic number 19).
Those two electrons fill the 3s orbital, which holds a maximum of two electrons. Standard filling order.
How many ml values are possible for l = 3?
Seven values of ml are possible when l = 3, ranging from –3 to +3 in integer steps.
Each integer in that range corresponds to a different magnetic quantum number for the f orbitals. Seven orbitals, seven ml values.
How many electrons can fit in the orbital for which l = 1 and n = 3?
Two electrons can fit in any single orbital, regardless of n and l.
Each orbital, defined by a unique set of n, l, and ml, is limited to two electrons with opposite spins. Pauli exclusion in action.
What is the shape of an orbital if the value of L = 2?
A clover-leaf or double-dumbbell shape — that’s the hallmark of a d-orbital.
Visualize two dumbbells crossing at right angles; that’s the basic look you’ll meet in chemistry textbooks. No need to overcomplicate it.
What is the maximum number of electrons in n = 4, L = 3?
Fourteen electrons can be represented by the values n = 4 and l = 3.
That’s the 4f subshell, with seven orbitals each holding two electrons. Total comes to fourteen — textbook case.
How many electrons can fit in the orbital for which l = 1 and n = 3?
Each orbital can hold two electrons — that’s the universal limit.
No matter what n and l are, one orbital = two electrons, period. Pauli exclusion doesn’t play favorites.
