Question

subshells & their orbitals

1. describe the shape each subshell and sketch the shape of their orbitals.

	s orbital	p orbitals
sketch

describing shells
consider the $n = 4$ shell of an atom.

1. how many subshells are in this shell? what are they?

1. how many orbitals are in this shell?

1. how many electrons could occupy this shell?

Explanation:

Step1: Answer subshell shape/description

S Orbital:

Description: Spherical, symmetric around nucleus.
Sketch: A single filled circle (or sphere outline) centered on a nucleus point.

P Orbitals:

Description: Dumbbell-shaped, three mutually perpendicular orientations ($p_x, p_y, p_z$), each with two lobes on opposite sides of the nucleus.
Sketch: Three separate dumbbell shapes: one aligned horizontally ($p_x$), one vertically ($p_y$), one along the depth axis ($p_z$), all centered on a nucleus point.

Step2: Find n=4 subshell count/names

For a shell with principal quantum number $n$, the number of subshells equals $n$, with azimuthal quantum numbers $l=0,1,...,n-1$.
$n=4$, so $l=0,1,2,3$ corresponding to $s, p, d, f$ subshells.
Count: $4$ subshells.

Step3: Calculate total orbitals in n=4

Total orbitals in a shell = $n^2$.
$n=4$, so $\text{Total orbitals} = 4^2 = 16$.

Step4: Calculate max electrons in n=4

Max electrons in a shell = $2n^2$.
$n=4$, so $\text{Max electrons} = 2\times4^2 = 32$.

Answer:

1.

Description	S Orbital	P Orbitals
Sketch	A single centered sphere outline	Three separate dumbbell outlines, aligned along x, y, z axes, all centered on a nucleus point

1. Number of subshells: 4; The subshells are the 4s, 4p, 4d, and 4f subshells.
2. 16
3. 32