The number of given orbitals which have electron density along the axis is _________
pₓ,p_y,p_z,d_(xy),d_(yz),d_(xz),d_(z²),d_(x²-y²)

Solution

Chemistry ma’am · 2 steps

Read the subscript: if it names an axis, the lobes sit on that axis; if it names a plane, they sit between.

1. What to check. An orbital has electron density along an axis when its lobes point straight along x, y or z. If the lobes point between two axes, the density on the axes themselves is zero.

   Orbital	Where the lobes point	Along an axis?
   pₓ, p_y, p_z	along x, y, z respectively	yes, 3
   d_(xy), d_(yz), d_(xz)	at 45°, between the two named axes	no, 0
   d_(z²)	two lobes along z, plus a ring in the xy plane	yes, 1
   d_(x²-y²)	four lobes along x and y	yes, 1

2. So. The three p orbitals plus d_(z²) and d_(x²-y²) give 3 + 1 + 1 = 5.

The common slip: 4. Leaving out d_(z²) because of its ring in the xy plane gives 4. Its two main lobes lie right along the z axis, so it counts.

The idea to keep. Squares in the subscript (z², x²-y²) mean lobes on the axes. Products (xy, yz, xz) mean lobes between the axes. Every p orbital lies on its own axis.

Answer from the NTA final answer key. Solution by PrepWiser.